A marketing analyst is studying the variability in customer purchase amounts bet

Question

A marketing analyst is studying the variability in customer purchase amounts between shopping mall stores and “big box” discount stores. She suspects the variability is different between those stores due to the nature of customers involved. To investigate this issue in detail, she compiled two random samples each consisting of 26 purchase amounts at shopping mall stores and discount stores. Use Table 4.

Select the appropriate hypotheses to test whether the variance of the purchase amounts differs between the two types of stores.

Construct the 90% confidence interval for the ratio of the population variances. Assume the purchase amount distributions are normally distributed. (Round "F" value and final answers to 2 decimal places.)

Use the computed confidence interval to test whether the variance of the purchase amounts differs between the two stores at the 10% significance level.

Confirm your conclusion using Excel’s F.TEST function to calculate the p-value. (Round your answer to 4 decimal places.)

A marketing analyst is studying the variability in customer purchase amounts between shopping mall stores and “big box” discount stores. She suspects the variability is different between those stores due to the nature of customers involved. To investigate this issue in detail, she compiled two random samples each consisting of 26 purchase amounts at shopping mall stores and discount stores. Use Table 4.

Explanation / Answer

a. Null Hypothesis : H0: 12 / 22 = 1,

Alternative Hypothesis : HA: 12 / 22 1

As we have 1 = standard deviation of population 1 shopping mall store purchase

2 = standard deviation of population 2 discount store purchase

as it is hypothesis test for only difference in variance not for which variance is higher or lower so we are using two tailed hypothesis test that's why we have discarded other two options.

b. 90% confidence interval for the ratio of the population variances.

Here F - value = s1 2 / s2 2

where s1 = standard deviation of sample 1 (shopping mall store purchase) = 78.3153

and s2 = standard deviation of sample 2 ( discount store purchase)= 36.5358

so F = (78.3153)2 / (36.5358)2 = 4.59

so confidence interval for the ratio of population variance ( 12 / 22) is

Lower Limt = (s1 2 / s2 2 )/ F1 - (/2) = 4.59/ F0.975,25,25 = 4.59/2.23 = 2.06

Upper Limit =  (s1 2 / s2 2 )/ F(/2) = 4.59/F0.025,25,25 = 4.59/0.45 = 10.24

so 2.06 < 12 / 22 < 10.24

(c) The 90% confidence interval does not contain the value 1, we reject H0 and conclude that the population variances in purchase amounts are different between shopping mall stores and “big box” retail stores.

(d) I have used the F. Test function and found P - value = 0.000302

The p-value is 0.000302. Thus, our conclusion agrees with the confidence interval approach in Part c.

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