Sample Mean Differences and Standard Deviation As a member of the marketing team for a pasta manufacturer, you want to find out whether there’s any difference in the mean number of people who would buy the new macaroni product, L-Bow Roni, if it had a red box and if it had a blue box.

In each session, you bring in 30 people to try L-Bow Roni and have them respond with whether they would buy this product over the competitor’s product. Suppose you conducted 45 sessions with the red box and 60 sessions with the blue box. This data sheet gives you the number of yes responses to the survey for each session. Note that the two samples are different sizes.

To determine whether this difference is significant, you need to find the standard deviation of the sample mean differences. For this task, you’ll use this formula for the standard deviation of sample mean differences.

In this formula, the subscripts and represent the means of the two samples, and are the standard deviations of the two populations, and and are the sample sizes.

Part A
Question
Use the spreadsheet’s Average function (look under AutoSum in the Function menu) to calculate the means.

Enter the correct value in each box. Use numerals instead of words, and round each value to the nearest hundredth.

The mean value of people who would purchase the red box is
.

The mean value of people who would purchase the blue box is
.

Part B
Question
What is the difference of the sample means of those who would purchase the red box and those who would purchase the blue box?

1.39
2.08
1.86
1.74
Part C
Question
Use the standard deviation values of the two samples to find the standard deviation of the sample mean differences.

Sample Standard Deviation
red box 3.868
blue box 2.933
Then complete each statement.

The sample size of the session regarding the number of people would purchase the red box, , is
.

The sample size of the session regarding the number of people would purchase the blue box , , is
.

The standard deviation of the sample mean differences is approximately
.