This is statistics....math.Homework 6...

Question

This is statistics....math.Homework 6 https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-quantitative-means/one-sample-t-interval-mean/v/confidence-interval-for-a-mean-difference https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-categorical-proportions/introduction-confidence-intervals/v/confidence-intervals-and-margin-of-error Directions: 1. Half credit for late work when submitted within one calendar week of the due date. 2. Open book, open notes, open collaboration. Try to do the problems without using the Internet. 3. Do your own work. Write up your own solution, even though you may collaborate and discuss the solution with other individuals. That is, do not copy another student’s work. 4. Show your steps/work to earn credits. 5. Copy question and write your solution on separate paper. 6. Scan your paper as PDF file and upload file to Canvas. 	Data set to be used with question #1: 6.42, 6.76, 6.56, 4.8, 8.43, 7.49, 8.05, 5.05, 5.77, 3.91, 6.77, 6.44, 6.17, 7.67, 7.34, 6.85, 5.13, 5.73 The distribution of this data set is taken from a normal distribution with some unknown mean μ and known variance σ2=1.42. 	1. Compute the point estimate (i.e.  of the mean μ from the data sample and the probability of the random variable is below 90% of the estimate: Pr () 	 Question #2 pertain to these data sets: 15.82,11.44,16.39,12.76,13.22,14.15,12.25,12.53,9.92,16.01,8.92,14.66,13.03,3.65,11.03,10.76,13.12,14.25, 13.1,18.49	 (σ2 = 6.25) 21.93,12.08,9.84,17.13,10.76,12.03,9.89,19.44,21.91,14.18,10.14,15.14,16.37,11.84,13.90,14.20,13.12,14.43, 15.74,17.33	 (σ2 = 25) The data set is taken from normal distribution with some unknown mean μ, but known variance as shown. When the variance of the population distribution is known the formula for computing confidence interval of population mean μ becomes  which is based on the standard normal (Z) table – instead of the t table. 	8. Compute (a) The 90% confidence interval for the population mean μ for each sample. (b) Being that the 2 intervals from these 2 samples overlap slightly because the sample mean of the 1st data set is “too” large (or that of the 2nd data set is “too” small), one can conceive a situation where the overlap would not occur for some other data samples. What can the largest value of the sample mean for the 1st data set be (given the same 2nd data set), in order to ensure that the 2 intervals do not overlap? 	9. Suppose that an intern calculated the point estimate of the population standard deviation of the weights of juvenile fish (of some kind) is 0.0125 grams, and the 95% confidence interval is (0.0086g,0.0228g), where the weights is known to be approximately a normal distribution. In his report of the data, the intern uses the point estimate of 0.0125g. On the other hand, his faculty adviser uses a value of 0.015g in her discussion of the finding. Discuss whether or not one of them is making an error. Homework 6   https://www.khanacademy.org/math/ap - statistics/xfb5d8e68:inference - quantitative - means/one - sample - t - interval - mean/v/confidence - interval - for - a - mean - difference  https://www.khanacademy.org/math/ap - statistics/xfb5d8e68:inferenc e - categorical - proportions/introduction - confidence - intervals/v/confidence - intervals - and - margin - of - error  Directions:   1.   Half credit for late work when submitted within one calendar week of the due date.   2.   Open book, open notes, open collaboration. Try to do the problems without using the Internet.   3.   Do your own work. Write up your own solution, even though you may collaborate and discuss  the solution with other individuals. That is, do not copy another student’s work.   4.   Show your steps/work to earn credits.   5.   Copy question and write your solution on separ ate paper.   6.   Scan your paper as PDF file and upload file to Canvas.  Data set to be used with question #1:   6.42, 6.76, 6.56, 4.8, 8.43, 7.49, 8.05, 5.05, 5.77, 3.91, 6.77, 6.44, 6.17, 7.67, 7.34, 6.85, 5.13, 5.73   The distribution of this data set is taken fr om a normal distribution with some unknown mean  μ   and known  variance  σ 2 =1.42.   1.   Compute the point estimate (i.e.  ?? ? = 1 ?? s ?? ?? = 1 ?? ?? )   of the mean  μ   from the data sample and the  probability of the random variable is below 90% of the estimate:   Pr ( X ? = 0 . 9 ?? ? )  Que stion #2 pertain to these data sets:   15.82,11.44,16.39,12.76,13.22,14.15,12.25,12.53,9.92,16.01,8.92,14.66,13.03,3.65,11.03,10.76,13.12,14.25,   13.1,18.49  (σ 2   = 6.25)  21.93,12.08,9.84,17.13,10.76,12.03,9.89,19.44,21.91,14.18,10.14,15.14,16.37,11.84,13.90,14.20,13.12,14.43,   15.74,17.33  (σ 2   = 25)   The data set is taken from normal distribution with some unknown mean  μ,   but known variance as shown.  When the variance of th e population distribution is known the formula for computing confidence interval of  population mean  μ   becomes  | ?? ? - ?? |

Atreye · Accepted Answer

Solution 1:
The point estimate of the mean of the sample is calculated as below:
The probability that a random variable is below 90% of the estimate of the mean is calculated as below:
Therefore, the required probability is 0.011245.
Solution 2:
(a)
The point estimate of the mean of the first sample is calculated as below:
The point estimate of the mean of the second sample is calculated as below:
The 90% confidence interval for the population mean for first sample is calculated as below:

Homework 6 https://www.khanacademy.org/math/ap-statistics/xfb5d8e68:inference-quantitative-means/one-sample-t-interval-mean/v/confidence-interval-for-a-mean-difference...

Answer To: Homework 6...

Answer To This Question Is Available To Download

Related Questions & Answers

Submit New Assignment