Question

In: Statistics and Probability

J.J.Bean sells a wide variety of outdoor equipment and clothing. The company sells both through mail...

J.J.Bean 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 1717 sales receipts for mail-order sales results in a mean sale amount of $78.60$⁢78.60 with a standard deviation of $24.75$⁢24.75. A random sample of 99 sales receipts for internet sales results in a mean sale amount of $72.10$⁢72.10 with a standard deviation of $25.25$⁢25.25. Using this data, find the 99%99% 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 2 of 3 :  

Find the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.

Solutions

Expert Solution

The data is given for the company sells through mail-order purchase and via Internet purchase .

Mail-order purchase Internet purchase
sample mean
sample standard deviation
sample size

Let, true mean amount of mail-order purchase

   the mean amount of internet purchase

Calculation for 99% confidence interval for the true mean difference

For non-equal variance, the confidence interval is calculated as-

Degrees of freedom (df):

Critical value:

for 99% confidence interval,

So, the 99% confidence interval for the true mean difference for mail-order purchase and internet purchase is , i.e.,

Hence we are 99% confident that the confidence interval (-28.1878, 41.1878) contains the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases.

Margin of error:

The margin of error use in calculating the confidence interval is-

Margin of error for the 99% confidence interval is calculated to be as Margin of error=34.687848


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