6.
–/1.29 points
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My Notes
Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml).
The sample mean isx≈94.4. Letxbe a random variable representing glucose readings taken from Gentle Ben. We may assume thatxhas a normal distribution, and we know from past experience thatσ= 12.5.The mean glucose level for horses should beμ= 85 mg/100 ml.†Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Useα= 0.05.
(a) What is the level of significance?
State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?
H
0:μ= 85;H
1:μ≠85; two-tailedH
0:μ= 85;H
1:μ> 85; right-tailedH
0:μ= 85;H
1:μ
H
0:μ> 85;H
1:μ= 85; right-tailed
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
The standard normal, since we assume thatxhas a normal distribution with knownσ.The Student'st, sincenis large with unknownσ.The standard normal, since we assume thatxhas a normal distribution with unknownσ.The Student'st, since we assume thatxhas a normal distribution with knownσ.
Compute thezvalue of the sample test statistic. (Round your answer to two decimal places.)
(c) Find (or estimate) theP-value. (Round your answer to four decimal places.)
Sketch the sampling distribution and show the area corresponding to theP-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at levelα?
At theα= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At theα= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At theα= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At theα= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) State your conclusion in the context of the application.
There is sufficient evidence at the 0.05 level to conclude that Gentle Ben's glucose is higher than 85 mg/100 ml.There is insufficient evidence at the 0.05 level to conclude that Gentle Ben's glucose is higher than 85 mg/100 ml.
7.
–/1.29 points
0/100 Submissions UsedBBUnderStat12 8.1.024.
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My Notes
Total blood volume (in ml) per body weight (in kg) is important in medical research. For healthy adults, the red blood cell volume mean is aboutμ= 28 ml/kg.†Red blood cell volume that is too low or too high can indicate a medical problem. Suppose that Roger has had seven blood tests, and the red blood cell volumes were as follows.
The sample mean isx≈32.7ml/kg. Letxbe a random variable that represents Roger's red blood cell volume. Assume thatxhas a normal distribution andσ= 4.75.Do the data indicate that Roger's red blood cell volume is different (either way) fromμ= 28 ml/kg?Use a0.01 levelof significance.
(a) What is the level of significance?
State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?
H
0:μ= 28 ml/kg;H
1:μ≠28 ml/kg; two-tailedH
0:μ= 28 ml/kg;H
1:μ
H
0:μ= 28 ml/kg;H
1:μ> 28 ml/kg; right-tailedH
0:μ≠28 ml/kg;H
1:μ= 28 ml/kg; two-tailed
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
The Student'st, since we assume thatxhas a normal distribution with knownσ.The standard normal, since we assume thatxhas a normal distribution with unknownσ.The Student'st, sincenis large with unknownσ.The standard normal, since we assume thatxhas a normal distribution with knownσ.
Compute thezvalue of the sample test statistic. (Round your answer to two decimal places.)
(c) Find (or estimate) theP-value. (Round your answer to four decimal places.)
Sketch the sampling distribution and show the area corresponding to theP-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at levelα?
At theα= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At theα= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.At theα= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At theα= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) State your conclusion in the context of the application.
There is sufficient evidence at the 0.01 level to conclude that Roger's average red cell volume differs from the average for healthy adults.There is insufficient evidence at the 0.01 level to conclude that Roger's average red cell volume differs from the average for healthy adults.
A random sample of25values is drawn from a mound-shaped and symmetric distribution. The sample mean is13and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is12.5.
(a) Is it appropriate to use a Student'stdistribution? Explain.
Yes, because thexdistribution is mound-shaped and symmetric andσis unknown.No, thexdistribution is skewed left.No, thexdistribution is skewed right.No, thexdistribution is not symmetric.No,σis known.
How many degrees of freedom do we use?
(b) What are the hypotheses?
H
0:μ
H
1:μ= 12.5H
0:μ= 12.5;H
1:μ
H
0:μ> 12.5;H
1:μ= 12.5H
0:μ= 12.5;H
1:μ≠12.5H
0:μ= 12.5;H
1:μ> 12.5
(c) Compute thetvalue of the sample test statistic. (Round your answer to three decimal places.)
t=
(d) Estimate theP-value for the test.
P-value > 0.2500.100
P-value 0.050
P-value 0.010
P-value
P-value
(e) Do we reject or fail to rejectH
0?
At theα= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At theα= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At theα= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At theα= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(f) Interpret the results.
There is sufficient evidence at the 0.05 level to reject the null hypothesis.There is insufficient evidence at the 0.05 level to reject the null hypothesis.
11.
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0/100 Submissions UsedBBUnderStat12 8.2.011.
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My Notes
Weatherwiseis a magazine published by the American Meteorological Society. One issue gives a rating system used to classify Nor'easter storms that frequently hit New England and can cause much damage near the ocean. A severe storm has an average peak wave height ofμ= 16.4 feet for waves hitting the shore. Suppose that a Nor'easter is in progress at the severe storm class rating. Peak wave heights are usually measured from land (using binoculars) off fixed cement piers. Suppose that a reading of34waves showed an average wave height ofx=16.9feet. Previous studies of severe storms indicate thatσ= 3.5feet. Does this information suggest that the storm is (perhaps temporarily) increasing above the severe rating? Useα= 0.01.
(a) What is the level of significance?
State the null and alternate hypotheses.
H
0:μ> 16.4 ft;H
1:μ= 16.4 ftH
0:μ= 16.4 ft;H
1:μ> 16.4 ftH
0:μ
H
1:μ= 16.4 ftH
0:μ= 16.4 ft;H
1:μ
H
0:μ= 16.4 ft;H
1:μ≠16.4 ft
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
The Student'st, since the sample size is large andσis unknown.The standard normal, since the sample size is large andσis unknown.The standard normal, since the sample size is large andσis known.The Student'st, since the sample size is large andσis known.
What is the value of the sample test statistic? (Round your answer to two decimal places.)
(c) Estimate theP-value.
P-value > 0.2500.100
P-value 0.050
P-value 0.010
P-value
P-value
Sketch the sampling distribution and show the area corresponding to theP-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at levelα?
At theα= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At theα= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.At theα= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At theα= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
There is sufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating.There is insufficient evidence at the 0.01 level to conclude that the storm is increasing above the severe rating.
12.
–/1.29 points
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My Notes
Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake isμ= 19inches. However, a survey reported that of a random sample of46fish caught, the mean length wasx=18.5inches, with estimated standard deviations=2.9inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less thanμ= 19inches? Useα= 0.05.
(a) What is the level of significance?
State the null and alternate hypotheses.
H
0:μ= 19 in;H
1:μ≠19 inH
0:μ
H
1:μ= 19 inH
0:μ> 19 in;H
1:μ= 19 inH
0:μ= 19 in;H
1:μ
H
0:μ= 19 in;H
1:μ> 19 in
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
The Student'st, since the sample size is large andσis known.The standard normal, since the sample size is large andσis known.The standard normal, since the sample size is large andσis unknown.The Student'st, since the sample size is large andσis unknown.
What is the value of the sample test statistic? (Round your answer to three decimal places.)
(c) Estimate theP-value.
P-value > 0.2500.100
P-value 0.050
P-value 0.010
P-value
P-value
Sketch the sampling distribution and show the area corresponding to theP-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at levelα?
At theα= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At theα= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At theα= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At theα= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
There is sufficient evidence at the 0.05 level to conclude that the average fish length is less than 19 inches.There is insufficient evidence at the 0.05 level to conclude that the average fish length is less than 19 inches.
13.
–/1.29 points
0/100 Submissions UsedBBUnderStat12 8.2.015.
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My Notes
Socially conscious investors screen out stocks of alcohol and tobacco makers, firms with poor environmental records, and companies with poor labor practices. Some examples of "good," socially conscious companies are Johnson and Johnson, Dell Computers, Bank of America, and Home Depot. The question is, are such stocks overpriced? One measure of value is the P/E, or price-to-earnings ratio. High P/E ratios may indicate a stock is overpriced. For the S&P Stock Index of all major stocks, the mean P/E ratio isμ= 19.4. A random sample of36"socially conscious" stocks gave a P/E ratio sample mean ofx=17.8,with sample standard deviations=5.4.Does this indicate that the mean P/E ratio of all socially conscious stocks is different (either way) from the mean P/E ratio of the S&P Stock Index? Useα= 0.05.
(a) What is the level of significance?
State the null and alternate hypotheses.
H
0:μ≠19.4;H
1:μ= 19.4H
0:μ= 19.4;H
1:μ
H
0:μ= 19.4;H
1:μ> 19.4H
0:μ= 19.4;H
1:μ≠19.4H
0:μ> 19.4;H
1:μ= 19.4
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
The Student'st, since the sample size is large andσis known.The standard normal, since the sample size is large andσis known.The standard normal, since the sample size is large andσis unknown.The Student'st, since the sample size is large andσis unknown.
What is the value of the sample test statistic? (Round your answer to three decimal places.)
(c) Estimate theP-value.
P-value > 0.2500.100
P-value 0.050
P-value 0.010
P-value
P-value
Sketch the sampling distribution and show the area corresponding to theP-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at levelα?
At theα= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At theα= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At theα= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At theα= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
There is sufficient evidence at the 0.05 level to conclude that the mean P/E ratio of all socially conscious stocks differs from the mean P/E ratio of the S&P Stock Index.There is insufficient evidence at the 0.05 level to conclude that the mean P/E ratio of all socially conscious stocks differs from the mean P/E ratio of the S&P Stock Index.
14.
–/1.29 points
0/100 Submissions UsedBBUnderStat12 8.2.016.
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My Notes
Unfortunately, arsenic occurs naturally in some ground water†. A mean arsenic level ofμ= 8.0parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of41tests gave a sample mean ofx=7.0ppb arsenic, withs=2.6ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Useα= 0.01.
(a) What is the level of significance?
State the null and alternate hypotheses.
H
0:μ= 8 ppb;H
1:μ≠8 ppbH
0:μ= 8 ppb;H
1:μ> 8 ppbH
0:μ> 8 ppb;H
1:μ= 8 ppbH
0:μ
H
1:μ= 8 ppbH
0:μ= 8 ppb;H
1:μ
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
The Student'st, since the sample size is large andσis unknown.The standard normal, since the sample size is large andσis unknown.The standard normal, since the sample size is large andσis known.The Student'st, since the sample size is large andσis known.
What is the value of the sample test statistic? (Round your answer to three decimal places.)
(c) Estimate theP-value.
P-value > 0.2500.100
P-value 0.050
P-value 0.010
P-value
P-value
Sketch the sampling distribution and show the area corresponding to theP-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at levelα?
At theα= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At theα= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.At theα= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At theα= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
There is sufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than 8 ppb.There is insufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than 8 ppb.
15.
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0/100 Submissions UsedBBUnderStat12 8.2.017.
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My Notes
Letxbe a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Thenxhas a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of thexdistribution is about4.74. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are as follows.
(i) Use a calculator with sample mean and standard deviation keys to findxands. (Round your answers to two decimal places.)
(ii) Do the given data indicate that the population mean RBC count for this patient is lower than4.74? Useα= 0.05.
(a) What is the level of significance?
State the null and alternate hypotheses.
H
0:μ= 4.74;H
1:μ
H
0:μ> 4.74;H
1:μ= 4.74H
0:μ= 4.74;H
1:μ> 4.74H
0:μ= 4.74;H
1:μ≠4.74H
0:μ
H
1:μ= 4.74
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
The Student'st, since we assume thatxhas a normal distribution andσis unknown.The standard normal, since we assume thatxhas a normal distribution andσis unknown.The standard normal, since we assume thatxhas a normal distribution andσis known.The Student'st, since we assume thatxhas a normal distribution andσis known.
What is the value of the sample test statistic? (Round your answer to three decimal places.)
(c) Estimate theP-value.
P-value > 0.2500.100
P-value 0.050
P-value 0.010
P-value
P-value
Sketch the sampling distribution and show the area corresponding to theP-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at levelα?
At theα= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At theα= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At theα= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At theα= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
There is sufficient evidence at the 0.05 level to conclude that the population mean RBC count for the patient is lower than 4.74.There is insufficient evidence at the 0.05 level to conclude that the population mean RBC count for the patient is lower than 4.74.
16.
–/1.29 points
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My Notes
Letxbe a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Thenxhas a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient's doctor are as follows.
(i) Use a calculator with sample mean and standard deviation keys to findxands. (Round your answers to two decimal places.)
(ii) Does this information indicate that the population average HC for this patient is higher than 14? Useα= 0.01.
(a) What is the level of significance?
State the null and alternate hypotheses.
H
0:μ= 14;H
1:μ
H
0:μ= 14;H
1:μ≠14H
0:μ= 14;H
1:μ> 14H
0:μ> 14;H
1:μ= 14H
0:μ
H
1:μ= 14
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
The Student'st, since we assume thatxhas a normal distribution andσis unknown.The Student'st, since we assume thatxhas a normal distribution andσis known.The standard normal, since we assume thatxhas a normal distribution andσis unknown.The standard normal, since we assume thatxhas a normal distribution andσis known.
What is the value of the sample test statistic? (Round your answer to three decimal places.)
(c) Estimate theP-value.
P-value > 0.2500.100
P-value 0.050
P-value 0.010
P-value
P-value
Sketch the sampling distribution and show the area corresponding to theP-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at levelα?
At theα= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At theα= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.At theα= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At theα= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
There is sufficient evidence at the 0.01 level to conclude that the population average HC for this patient is higher than 14.There is insufficient evidence at the 0.01 level to conclude that the population average HC for this patient is higher than 14.
17.
–/1.29 points
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My Notes
A national newspaper reported that the state with the longest mean life span is Hawaii, where the population mean life span is76years. A random sample of 20 obituary notices in theHonolulu Advertizergave the following information about life span (in years) of Honolulu residents.
72
|
68
|
81
|
93
|
56
|
19
|
78
|
94
|
83
|
84
|
77
|
69
|
85
|
97
|
75
|
71
|
86
|
47
|
66
|
27
|
(i) Use a calculator with sample mean and standard deviation keys to findxands. (Round your answers to two decimal places.)
(ii) Assuming that life span in Honolulu is approximately normally distributed, does this information indicate that the population mean life span for Honolulu residents is less than76years? Use a 5% level of significance.
(a) What is the level of significance?
State the null and alternate hypotheses.
H
0:μ> 76 yr;H
1:μ= 76 yrH
0:μ= 76 yr;H
1:μ
H
0:μ= 76 yr;H
1:μ≠76 yrH
0:μ
H
1:μ= 76 yrH
0:μ= 76 yr;H
1:μ> 76 yr
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
The Student'st, since we assume thatxhas a normal distribution andσis unknown.The Student'st, since we assume thatxhas a normal distribution andσis known.The standard normal, since we assume thatxhas a normal distribution andσis known.The standard normal, since we assume thatxhas a normal distribution andσis unknown.
What is the value of the sample test statistic? (Round your answer to three decimal places.)
(c) Estimate theP-value.
P-value > 0.2500.100
P-value 0.050
P-value 0.010
P-value
P-value
Sketch the sampling distribution and show the area corresponding to theP-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at levelα?
At theα= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At theα= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At theα= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At theα= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
There is sufficient evidence at the 0.05 level to conclude that the population mean life span of Honolulu residents is less than 76 years.There is insufficient evidence at the 0.05 level to conclude that the population mean life span of Honolulu residents is less than 76 years.
19.
–/1.29 points
0/100 Submissions UsedBBUnderStat12 8.3.005.MI.
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My Notes
A random sample of30binomial trials resulted in12successes. Test the claim that the population proportion of successes does not equal 0.50. Use a level of significance of 0.05.
(a) Can a normal distribution be used for thep̂distribution? Explain.
No,npis greater than 5, butnqis less than 5.Yes,npandnqare both less than 5.No,nqis greater than 5, butnpis less than 5.Yes,npandnqare both greater than 5.No,npandnqare both less than 5.
(b) State the hypotheses.
H
0:p
H
1:p= 0.5H
0:p= 0.5;H
1:p
H
0:p= 0.5;H
1:p> 0.5H
0:p= 0.5;H
1:p≠0.5
(c) Computep̂.
Compute the corresponding standardized sample test statistic. (Round your answer to two decimal places.)
(d) Find theP-value of the test statistic. (Round your answer to four decimal places.)
(e) Do you reject or fail to reject
H
0?
Explain.
At theα= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At theα= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At theα= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At theα= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(f) What do the results tell you?
The samplep̂value based on 30 trials is not sufficiently different from 0.50 to not rejectH
0forα= 0.05.The samplep̂value based on 30 trials is sufficiently different from 0.50 to justify rejectingH
0forα= 0.05.The samplep̂value based on 30 trials is sufficiently different from 0.50 to not rejectH
0forα= 0.05.The samplep̂value based on 30 trials is not sufficiently different from 0.50 to justify rejectingH
0forα= 0.05.
20.
–/1.29 points
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My Notes
Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are the auditor for a very large corporation. The revenue file contains millions of numbers in a large computer data bank. You draw a random sample ofn=226numbers from this file andr=87have a first nonzero digit of 1. Letprepresent the population proportion of all numbers in the computer file that have a leading digit of 1.
(i) Test the claim thatpis more than 0.301. Useα=0.10.
(a) What is the level of significance?
State the null and alternate hypotheses.
H
0:p= 0.301;H
1:p> 0.301H
0:p= 0.301;H
1:p
H
0:p> 0.301;H
1:p= 0.301H
0:p= 0.301;H
1:p≠0.301
(b) What sampling distribution will you use?
The Student'st, sincenp
nqThe Student'st, sincenp> 5 andnq> 5.The standard normal, sincenp
nqThe standard normal, sincenp> 5 andnq> 5.
What is the value of the sample test statistic? (Round your answer to two decimal places.)
(c) Find theP-value of the test statistic. (Round your answer to four decimal places.)
Sketch the sampling distribution and show the area corresponding to theP-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at levelα?
At theα= 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.At theα= 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant.At theα= 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At theα= 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
There is sufficient evidence at the 0.10 level to conclude that the true proportion of numbers with a leading 1 in the revenue file is greater than 0.301.There is insufficient evidence at the 0.10 level to conclude that the true proportion of numbers with a leading 1 in the revenue file is greater than 0.301.
(ii) Ifpis in fact larger than 0.301, it would seem there are too many numbers in the file with leading 1's. Could this indicate that the books have been "cooked" by artificially lowering numbers in the file? Comment from the point of view of the Internal Revenue Service. Comment from the perspective of the Federal Bureau of Investigation as it looks for "profit skimming" by unscrupulous employees.
Yes. There seems to be too many entries with a leading digit 1.No. There seems to be too many entries with a leading digit 1.Yes. There does not seem to be too many entries with a leading digit 1.No. There does not seem to be too many entries with a leading digit 1.
(iii) Comment on the following statement: If we reject the null hypothesis at level of significanceα, we have not provedH
0to be false. We can say that the probability isαthat we made a mistake in rejectingHo
. Based on the outcome of the test, would you recommend further investigation before accusing the company of fraud?
We have not provedH
0to be false. Because our data lead us to reject the null hypothesis, more investigation is not merited.We have not provedH
0to be false. Because our data lead us to reject the null hypothesis, more investigation is merited.We have not provedH
0to be false. Because our data lead us to accept the null hypothesis, more investigation is not merited.We have provedH
0to be false. Because our data lead us to reject the null hypothesis, more investigation is not merited.
21.
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0/100 Submissions UsedBBUnderStat12 8.3.009.
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My Notes
Is the national crime rate really going down? Some sociologists say yes! They say that the reason for the decline in crime rates in the 1980s and 1990s is demographics. It seems that the population is aging, and older people commit fewer crimes. According to the FBI and the Justice Department, 70% of all arrests are of males aged 15 to 34 years†. Suppose you are a sociologist in Rock Springs, Wyoming, and a random sample of police files showed that of37arrests last month,21were of males aged 15 to 34 years. Use a5%level of significance to test the claim that the population proportion of such arrests in Rock Springs is different from 70%.
(a) What is the level of significance?
State the null and alternate hypotheses.
H
0:p
H
1:p= 0.7H
0:p= 0.7;H
1:p> 0.7H
0:p= 0.7;H
1:p≠0.7H
0:p≠0.7;H
1:p= 0.7H
0:p= 0 .7;H
1:p
(b) What sampling distribution will you use?
The standard normal, sincenp
nqThe Student'st, sincenp> 5 andnq> 5.The standard normal, sincenp> 5 andnq> 5.The Student'st, sincenp
nq
What is the value of the sample test statistic? (Round your answer to two decimal places.)
(c) Find theP-value of the test statistic. (Round your answer to four decimal places.)
Sketch the sampling distribution and show the area corresponding to theP-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at levelα?
At theα= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At theα= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At theα= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At theα= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
There is sufficient evidence at the 0.05 level to conclude that the true proportion of arrests of males aged 15 to 34 in Rock Springs differs from 70%.There is insufficient evidence at the 0.05 level to conclude that the true proportion of arrests of males aged 15 to 34 in Rock Springs differs from 70%.
22.
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0/100 Submissions UsedBBUnderStat12 8.3.012.
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My Notes
What is your favorite color? A large survey of countries, including the United States, China, Russia, France, Turkey, Kenya, and others, indicated that most people prefer the color blue. In fact, about 24% of the population claim blue as their favorite color.†Suppose a random sample ofn=55college students were surveyed andr=8of them said that blue is their favorite color. Does this information imply that the color preference of all college students is different (either way) from that of the general population? Useα= 0.05.
(a) What is the level of significance?
State the null and alternate hypotheses.
H
0:p= 0.24;H
1:p
H
0:p= 0.24;H
1:p> 0.24H
0:p≠0.24;H
1:p= 0.24H
0:p= 0.24;H
1:p≠0.24
(b) What sampling distribution will you use?
The Student'st, sincenp> 5 andnq> 5.The standard normal, sincenp> 5 andnq> 5.The Student'st, sincenp
nqThe standard normal, sincenp
nq
What is the value of the sample test statistic? (Round your answer to two decimal places.)
(c) Find theP-value of the test statistic. (Round your answer to four decimal places.)
Sketch the sampling distribution and show the area corresponding to theP-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at levelα?
At theα= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At theα= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At theα= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At theα= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
There is sufficient evidence at the 0.05 level to conclude that the true proportion of college students favoring the color blue differs from 0.24.There is insufficient evidence at the 0.05 level to conclude that the true proportion of college students favoring the color blue differs from 0.24.
23.
–/1.29 points
0/100 Submissions UsedBBUnderStat12 8.3.013.
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My Notes
The following is based on information fromThe Wolf in the Southwest: The Making of an Endangered Species, by David E. Brown (University of Arizona Press). Before 1918, the proportion of female wolves in the general population of all southwestern wolves was about 50%. However, after 1918, southwestern cattle ranchers began a widespread effort to destroy wolves. In a recent sample of37wolves, there were only11females. One theory is that male wolves tend to return sooner than females to their old territories, where their predecessors were exterminated. Do these data indicate that the population proportion of female wolves is now less than 50% in the region? Useα= 0.01.
(a) What is the level of significance?
State the null and alternate hypotheses.
H
0:p= 0.5;H
1:p
H
0:p
H
1:p= 0.5H
0:p= 0.5;H
1:p> 0.5H
0:p= 0.5;H
1:p≠0.5
(b) What sampling distribution will you use?
The standard normal, sincenp> 5 andnq> 5.The Student'st, sincenp
nqThe standard normal, sincenp
nqThe Student'st, sincenp> 5 andnq> 5.
What is the value of the sample test statistic? (Round your answer to two decimal places.)
(c) Find theP-value of the test statistic. (Round your answer to four decimal places.)
Sketch the sampling distribution and show the area corresponding to theP-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at levelα?
At theα= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At theα= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.At theα= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At theα= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
There is sufficient evidence at the 1% level to conclude that the true proportion of female wolves in the region is less than 0.5.There is insufficient evidence at the 1% level to conclude that the true proportion of female wolves in the region is less than 0.5.
24.
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0/100 Submissions UsedBBUnderStat12 8.3.014.
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My Notes
In a fishing lodge brochure, the lodge advertises that 75% of its guests catch northern pike over 20 pounds. Suppose that last summer61out of a random sample of85guests did, in fact, catch northern pike weighing over 20 pounds. Does this indicate that the population proportion of guests who catch pike over 20 pounds is different from 75% (either higher or lower)? Useα= 0.05.
(a) What is the level of significance?
State the null and alternate hypotheses.
H
0:p= 0.75;H
1:p
H
0:p= 0.75;H
1:p> 0.75H
0:p= 0.75;H
1:p≠0.75H
0:p≠0.75;H
1:p= 0.75H
0:p
H
1:p= 0.75
(b) What sampling distribution will you use?
The standard normal, sincenp
nqThe standard normal, sincenp> 5 andnq> 5.The Student'st, sincenp> 5 andnq> 5.The Student'st, sincenp
nq
What is the value of the sample test statistic? (Round your answer to two decimal places.)
(c) Find theP-value of the test statistic. (Round your answer to four decimal places.)
Sketch the sampling distribution and show the area corresponding to theP-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at levelα?
At theα= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At theα= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.At theα= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At theα= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
There is sufficient evidence at the 0.05 level to conclude that the true proportion of guests who catch pike over 20 pounds differs from 75%.There is insufficient evidence at the 0.05 level to conclude that the true proportion of guests who catch pike over 20 pounds differs from 75%.
25.
–/1.29 points
0/100 Submissions UsedBBUnderStat12 8.3.015.
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My Notes
Prose rhythm is characterized as the occurrence of five-syllable sequences in long passages of text. This characterization may be used to assess the similarity among passages of text and sometimes the identity of authors. The following information is based on an article by D. Wishart and S. V. Leach appearing inComputer Studies of the Humanities and Verbal Behavior(Vol. 3, pp. 90-99). Syllables were categorized as long or short. On analyzing Plato'sRepublic, Wishart and Leach found that about 26.1% of the five-syllable sequences are of the type in which two are short and three are long. Suppose that Greek archaeologists have found an ancient manuscript dating back to Plato's time (about 427 - 347 B.C.). A random sample of313five-syllable sequences from the newly discovered manuscript showed that60are of the type two short and three long. Do the data indicate that the population proportion of this type of five syllable sequence is different (either way) from the text of Plato'sRepublic? Useα= 0.01.
(a) What is the level of significance?
State the null and alternate hypotheses.
H
0:p= 0.261;H
1:p≠0.261H
0:p≠0.261;H
1:p= 0.261H
0:p= 0.261;H
1:p> 0.261H
0:p= 0.261;H
1:p
(b) What sampling distribution will you use?
The standard normal, sincenp
nqThe standard normal, sincenp> 5 andnq> 5.The Student'st, sincenp> 5 andnq> 5.The Student'st, sincenp
nq
What is the value of the sample test statistic? (Round your answer to two decimal places.)
(c) Find theP-value of the test statistic. (Round your answer to four decimal places.)
Sketch the sampling distribution and show the area corresponding to theP-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at levelα?
At theα= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At theα= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.At theα= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At theα= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
There is sufficient evidence at the 0.01 level to conclude that the true proportion of the five-syllable sequence differs from that of the text of Plato'sRepublic.There is insufficient evidence at the 0.01 level to conclude that the true proportion of the five-syllable sequence differs from that of the text of Plato'sRepublic.
26.
–/1.29 points
0/100 Submissions UsedBBUnderStat12 8.3.017.
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My Notes
USA Todayreported that about 47% of the general consumer population in the United States is loyal to the automobile manufacturer of their choice. Suppose Chevrolet did a study of a random sample of1005Chevrolet owners and found that489said they would buy another Chevrolet. Does this indicate that the population proportion of consumers loyal to Chevrolet is more than 47%? Useα= 0.01.
(a) What is the level of significance?
State the null and alternate hypotheses.
H
0:p= 0.47;H
1:p> 0.47H
0:p= 0.47;H
1:p≠0.47H
0:p= 0.47;H
1:p
H
0:p> 0.47;H
1:p= 0.47
(b) What sampling distribution will you use?
The Student'st, sincenp> 5 andnq> 5.The standard normal, sincenp> 5 andnq> 5.The Student'st, sincenp
nqThe standard normal, sincenp
nq
What is the value of the sample test statistic? (Round your answer to two decimal places.)
(c) Find theP-value of the test statistic. (Round your answer to four decimal places.)
Sketch the sampling distribution and show the area corresponding to theP-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at levelα?
At theα= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At theα= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.At theα= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At theα= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
There is sufficient evidence at the 0.01 level to conclude that the true proportion of customers loyal to Chevrolet is more than 0.47.There is insufficient evidence at the 0.01 level to conclude that the true proportion of customers loyal to Chevrolet is more than 0.47.