Question

Step 1 of 3: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places. 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 66 sales receipts for mail-order sales results in a mean sale amount of $83.00 with a standard deviation of $20.25. A random sample of 11 sales receipts for internet sales results in a mean sale amount of $72.60 with a standard deviation of $23.75. Using this data, find the 95% 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.
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 66 sales
receipts for mail-order sales results in a mean sale amount
of $83.00 with a standard deviation of $20.25. A
random sample of 11 sales receipts for internet sales
results in a mean sale amount of $72.60 with a standard
deviation of $23.75. Using this data, find
the 95% 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.

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Added by Shari A.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Sri K

05/10/2022

Step 1

Because the standard deviation of the population is unknown, we express the critical value as a t-score rather than a Z-score. To find the critical value, we need to know the degrees of freedom. The formula for degrees of freedom when population variances are Show more…

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Step 1 of 3: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places. 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 66 sales receipts for mail-order sales results in a mean sale amount of $83.00 with a standard deviation of $20.25. A random sample of 11 sales receipts for internet sales results in a mean sale amount of $72.60 with a standard deviation of $23.75. Using this data, find the 95% 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.

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Transcript

00:01 In this question they given here.

00:02 So the question which is related to, that is the values of x1 x2 and s1 s2.

00:14 But this information now we have to find out that is the critical value.

00:22 So first one, critical value and the second one.

00:30 So margin of error, which is margin of error, and final one, the confidence interval.

00:49 The confidence interval.

00:56 So these values we have to find out now.

00:59 So let's come to the solution.

01:05 From the given information, they given that, that is here x1 bar is equal to 83 comma, x2 bar is to 72 .60 and s1 is equal to 20 .25 comma s2 is equal to 23 .75 so let us calculate the first one that is the critical value so let's come to that so here is critical value which is d f is equal to here the formula is place s2 squared divided by n2 which is whole square the whole divided by so 1 divided by n minus 1 multiply by s 1 divided by n 1 whole square place similarly here 1 divided by n 2 minus 1 which one is divided by s 2 squared by n2 whole square so here from the given information we know the values of these terms so now let us subdue these values here which is is equal to that is so 20 .25 whole square divided by six plates and here 23 .75 whole square divided by 11 which is whole square divided by 1 divided by 6 minus 1 so here, 20 .25 whole square divided by 6 whole square plus 1 divided by 11 minus 1, 23 .75 whole square divided by 11 and whole square.

03:14 So after completion this process, this calculation here we will get that is here 14309.

03:22 Point 461 divided by here this value became 30934 .174 plus 262 .948 so this will is equal to that is 14 ,309 .461 divided by after this addition of these two values here we will get that is 1197 .1 double...

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