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Does the average time sleeping per night differ between citizens of Denver and the citizens of Nashville? The mean number of hours, ๐œ‡x, of nightly sleeping in Denver will be compared to the mean number of hours, ๐œ‡y of nightly sleeping in Nashville. The true values of ๐œ‡x and ๐œ‡y are unknown. It is recognized that the true standard deviations are ๐œŽx = 1.7 hours for the Denver area and ๐œŽy = 1.9 hours for the Nashville area. We tale a random sample of m = 28 Denver citizens and n = 32 Nashville citizens. The mean numbers of hours sleeping were x-bar = 7.6 hours for the Denver citizens and y-bar = 7.1 hours for the Nashville citizens. Assuming all measurements were independent from one another and assuming that sleeping times are normally distributed we would like to estimate ๐œ‡x โˆ’ ๐œ‡y (a) What is the standard deviation of the distribution of y-bar? (b) What is the standard deviation of the distribution of x-bar - y-bar? (c) Create a 96% confidence interval for ๐œ‡x โˆ’ ๐œ‡y? (d) What is the length of the confidence interval in part c (e) If we let n stay at 32 but vary m, what is the smallest m for which the length of the 96% confidence interval would be 1.5 or less? (f) Write out R script or any other comments for the above 

          Does the average time sleeping per night differ between citizens of Denver and the citizens of Nashville? The mean number of hours, ๐œ‡x, of nightly sleeping in Denver will be compared to the mean number of hours, ๐œ‡y of nightly sleeping in Nashville. The true values of ๐œ‡x and ๐œ‡y are unknown. It is recognized that the true standard deviations are ๐œŽx = 1.7 hours for the Denver area and ๐œŽy = 1.9 hours for the Nashville area. We tale a random sample of m = 28 Denver citizens and n = 32 Nashville citizens. The mean numbers of hours sleeping were x-bar = 7.6 hours for the Denver citizens and y-bar = 7.1 hours for the Nashville citizens. Assuming all measurements were independent from one another and assuming that sleeping times are normally distributed we would like to estimate ๐œ‡x โˆ’ ๐œ‡y

(a) What is the standard deviation of the distribution of y-bar?
(b) What is the standard deviation of the distribution of x-bar - y-bar?
(c) Create a 96% confidence interval for ๐œ‡x โˆ’ ๐œ‡y?
(d) What is the length of the confidence interval in part c
(e) If we let n stay at 32 but vary m, what is the smallest m for which the length of the 96% confidence interval would be 1.5 or less?
(f) Write out R script or any other comments for the above
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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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Does the average time sleeping per night differ between citizens of Denver and the citizens of Nashville? The mean number of hours, ๐œ‡x, of nightly sleeping in Denver will be compared to the mean number of hours, ๐œ‡y of nightly sleeping in Nashville. The true values of ๐œ‡x and ๐œ‡y are unknown. It is recognized that the true standard deviations are ๐œŽx = 1.7 hours for the Denver area and ๐œŽy = 1.9 hours for the Nashville area. We tale a random sample of m = 28 Denver citizens and n = 32 Nashville citizens. The mean numbers of hours sleeping were x-bar = 7.6 hours for the Denver citizens and y-bar = 7.1 hours for the Nashville citizens. Assuming all measurements were independent from one another and assuming that sleeping times are normally distributed we would like to estimate ๐œ‡x โˆ’ ๐œ‡y (a) What is the standard deviation of the distribution of y-bar? (b) What is the standard deviation of the distribution of x-bar - y-bar? (c) Create a 96% confidence interval for ๐œ‡x โˆ’ ๐œ‡y? (d) What is the length of the confidence interval in part c (e) If we let n stay at 32 but vary m, what is the smallest m for which the length of the 96% confidence interval would be 1.5 or less? (f) Write out R script or any other comments for the above
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Transcript

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00:01 Does the average time sleeping per night differ between citizens of denver and citizens of nashville? the mean number of hours of nightly sleeping in denver.
00:08 So i'm going to, instead of using their distinguishers, i'm just going to isolate these under denver and nashville.
00:17 My population standard deviation for denver is 1 .7.
00:20 I have a sample size of 28 and a sample mean of 7 .6.
00:26 For nashville, my population standard deviation is 1 .9.
00:28 I have a sample of 32 and i have a sample mean of 7 .1.
00:34 Assume all measurements are independent from one another and assume the sleeping times are normally distributed.
00:39 What is the standard deviation of the distribution of, in this case, of denver? so they say of y -bar, but y -bar is associated with denver, so 1 .7.
00:54 B, the standard deviation for nashville is 1 .9.
00:58 For c, create a 96 % confidence interval for the difference...
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