Question

Land's Bend sells a wide variety of outdoor equipment and clothing. The company sells both through mail order and via the internet. Random samples of sales receipts were studied for mail-order sales and internet sales, with the total purchase being recorded for each sale. A random sample of 1616 sales receipts for mail-order sales results in a mean sale amount of $72.50$⁢72.50 with a standard deviation of $20.75$⁢20.75. A random sample of 77 sales receipts for internet sales results in a mean sale amount of $80.80$⁢80.80 with a standard deviation of $15.75$⁢15.75. Using this data, find the 90%90% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases. Assume that the population variances are not equal and that the two populations are normally distributed.

Step 1 of 3 :  

Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answer 1

Let X1 be the random variable denoting mail total order amount.

Let X2 be the random variable denoting internet total order amount.
Given Information






(As all the values are doubly given, I've taken n1 and n2 as 16 and 7 respectively.)


The test statistic is given by


Under Null,


Then,
the 90% Confidence Interval is given by:





Now,
(Required Critical Value)





Hence, the required Confidence Interval is
(-21.889,5.289)

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