In a particular population, it was of interest whether donut shops are, on average, more profitable than ice cream shops. A random sample of firms was taken with their average annual sales (£k) given in the table below. Year 1 2 3 4 5 6 7 Donut shop 240 290 210 174 210 150 230 Ice cream shop 210 230 187 240 230 220 174 REQUIRED: Use the above data to calculate the mean and standard deviation for the annual sales for each of the two shops. Discuss whether there is evidence that the difference between the two shops sales is non-zero. You are told that the mean difference between the two shops sales is 1.86 and the standard deviation is 54.46. Obtain a 95% confidence interval for the mean difference in sales of the two shops. Compare the uses of the independent samples and paired samples t tests. Explain clearly in which circumstances each method should be used in preference to the other, illustrating your answer with appropriate examples. State briefly the appropriate assumptions made in each case.

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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In a particular population, it was of interest whether donut shops are, on average, more profitable than ice cream shops. A random sample of firms was taken with their average annual sales (£k) given in the table below.

REQUIRED:

Use the above data to calculate the mean and standard deviation for the annual sales for each of the two shops.
Discuss whether there is evidence that the difference between the two shops sales is non-zero.
You are told that the mean difference between the two shops sales is 1.86 and the standard deviation is 54.46. Obtain a 95% confidence interval for the mean difference in sales of the two shops.
Compare the uses of the independent samples and paired samples t tests. Explain clearly in which circumstances each method should be used in preference to the other, illustrating your answer with appropriate examples. State briefly the appropriate assumptions made in each case.

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