Eddie Clauer 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 8 sales receipts for mail-order sales results in a mean sale amount of $69.30 with a standard deviation of $26.25. A random sample of 17 sales receipts for internet sales results in a mean sale amount of $75.90 with a standard deviation of $28.25. Using this data, find the 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. 1. Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
2. Find the Staandard error of the sampling distrbution to be used in constructing the confidence interval

1. The critical value to be used for constructing the confidence interval is 1.415

2. The standard error of the sampling distribution to be used in constructing the confidence interval, is approximately 6.260

Step-by-step explanation:

The number of mail-order receipts, n₁ = 8 sales receipts

The mean amount of sale, = $69.30

The standard deviation of the sample, σ₁ = $26.25

The number of internet sales receipts, n₂ = 17 sales receipts

The mean amount of sale, = $75.90

The standard deviation of the sample, σ₂ = $28.25

1. Where the population variance are not equal, we have;

Where;

= The critical value for constructing the confidence interval

= The standard error for constructing the confidence interval

The degrees of freedom, df = n₁ - 1 = 8 - 1 = 7

The t-value at 90% confidence level, and degrees of freedom of 7, , from the tables is given as follows;

= = 1.415

The critical value for constructing the confidence interval = = 1.415

2. The standard error of the sampling distribution to be used in constructing the confidence interval, , is given as follows

≈ 6.260

The standard error of the sampling distribution to be used in constructing the confidence interval, ≈ 6.260

the results from a pre-test for students for the year 2000 and the year 2010 are illustrated in the box plot. what do these results tell us about how students performed on the 29 question pre-test for the two years?

if we compare only the lowest and highest scores between the two years, we might conclude that the students in 2010 did better than the students in 2010. this conclusion seems to follow since the lowest score of 8 in 2010 is greater in value than the lowest score of 6 in 2000. also, the highest score of 28 in 2010 is greater in value than the highest score of 27 in 2000.

but the box portion of the illustration gives us more detailed information. the middle bar in each box shows us that the median score of 20 in 2000 is greater in value than the median score of 17 in 2010. further, we note that the box and whiskers divide the illustration into four pieces. each of these four pieces represents the same portion of students. so, the upper half of the students in 2000 scored in the same score range as the upper one-fourth of the students in 2010, see the illustration at a score of 20.

by considering the upper one-fourth, upper half, and upper three-fourths instead of just the lowest and highest scores, we would conclude that the students as a whole did much better in 2000 than in 2010. we would conclude that as a whole the students in 2010 are less prepared than the students in 2000.

in this section, we discuss box-and-whisker plots and the five key values used in constructing a box-and-whisker plot. the key values are called a five-number summary, which consists of the minimum, first quartile, median, third quartile, and maximum.

step-by-step explanation: