Practice Problems
Use the following to answer questions 1-2:
Your restaurant will serve 50 dinner groups tonight. Assume that the mean check size of dinner groups in general $60, the standard deviation is $40, and the distribution is slightly skewed with a longer tail toward high values.
1.Find the mean and standard deviation of average of all 50 checks.
2.Find the probability that the average of all 50 checks is between $58 and $65, assuming normal distribution.
Use the following to answer questions 3-5:
A survey of 21 business intelligence analysts, who had been in their current positions from 10 to 20 years, revealed $90,734 as the average salary. Assume a random sample with a standard deviation of $15,000.
3.Find the 95% confidence interval for the population mean salary.
4.Find the 99% confidence interval for the population mean salary.
5.Complete the following sentence: We are 95% sure that the population mean salary is at least _________________.
Use the following to answer questions 6-7:
The administrator of a nursing home would like to do a time and motion study of staff time spent per day performing nonemergency tasks. Prior to the introduction of some efficiency measures, the average person hours per day spent on these tasks was u = 16. The administrator wants to test whether the efficiency measures have reduced the value of u.
6.Write the null and research hypothesis that is being tested.
7.How many days must be sampled to test the proposed hypothesis if she wants a test having alpha = 0.05 and probability of a Type II error of at most 0.1 when the actual value of u is 12 hours or less. Assume sigma = 7.64.
Use the following to answer questions 8-13:
Dave Bowen is Planning Manager for Gadgets Galore, a kitchen supply manufacturer.He has been asked to develop a sales prediction model. After collecting quarterly data on unit sales volume (100,000’s), advertising expenditures ($100,000’s), unit price ($), and the number of sales representatives employed, he prints out the following tables in Excel:
Correlation Matrix
SUMMARY OUTPUT
Regression Statistics
ANOVA
8.What are the Null hypothesis and the Research hypothesis to test the appropriateness of a linear model to estimate sales volume?
9.Using thepvalue method does Dave reject the Null hypothesis?
10.Which of the independent variables are statistically significant at the 5% level?
11.What is the estimated impact on sales from a $1.00 decrease in price?
12.What is the estimated impact on sales from the hiring of 10 new sales reps?
13.What is the measure of prediction error for this model?
Use the following to answer questions 14-17:
Jean Siskel is an entertainment analyst for West Coast Securities. He is trying to develop a model to estimate gross earnings generated by a new movie release.He has collected the following data on 20 movies: Gross Earnings, Production Costs, Promotion Costs, and if the movie is based on a bestseller novel:
|
Gross Earnings
|
Production Cost
|
Promotion Cost
|
|
Movie
|
Millions $
|
Millions $
|
Millions $
|
Novel
|
1
|
28
|
4.2
|
1
|
0
|
2
|
35
|
6
|
3
|
1
|
3
|
50
|
5.5
|
6
|
1
|
4
|
20
|
3.3
|
1
|
0
|
5
|
75
|
12.5
|
11
|
1
|
6
|
60
|
9.6
|
8
|
1
|
7
|
15
|
2.5
|
0.5
|
0
|
8
|
72
|
10
|
12
|
1
|
9
|
45
|
6.4
|
8
|
1
|
10
|
37
|
7.5
|
5
|
0
|
11
|
30
|
5.0
|
1
|
1
|
12
|
63
|
10.1
|
10
|
0
|
13
|
58
|
7.8
|
9
|
1
|
14
|
50
|
6.9
|
10
|
0
|
15
|
24
|
3.5
|
4
|
0
|
16
|
82
|
11.0
|
15
|
1
|
17
|
48
|
10.7
|
1
|
1
|
18
|
34
|
6.6
|
2
|
0
|
19
|
50
|
8.4
|
3
|
1
|
20
|
45
|
10.8
|
5
|
0
|
14.What type of variable is novel?
15.What is the estimated multiple linear regression equation derived from this data?
16.Interpret the regression coefficient for promotion cost.
17.Interpret the regression coefficient for novel.
Use the following to answer questions 18-19:
Educational Achievement Associates has taken a random sample of households in Everytown, Iowa.Their data on household income and highest level of education completed is summarized in the table below. The data was collected to test for independence of educational background with the household income.
18.State the null hypothesis and the research hypothesis for the study.
19.Do you reject the H0at the 2.5 % significance level?
Use the following to answer questions 20-22:
A drug manufacturer claims that for 50% of all the users of a certain drug, the condition will improve; 30% of all the users will show no change; 15% of the users will become slightly worse and 5% will become much worse.
A random test of the drug on people gave these results
Condition
|
Number
|
Improvement
|
90
|
No change
|
51
|
Slightly worse
|
41
|
Much worse
|
18
|
20.State the null hypothesis and the research hypothesis for the test results.
21.Do you reject the null hypothesis?
What can you say about the manufacturer's claim?