Question

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.

Answer 1

To assess if packaging color affects purchase intent for L-Bow Roni, we calculate the standard deviation of sample mean differences using sample means and standard deviations, but data is not provided to complete this calculation.

Step-by-step explanation:

To determine if there's a significant difference in the mean number of people who would buy the new macaroni product, L-Bow Roni, in red versus blue packaging, we will calculate the standard deviation of the sample mean differences using the formula provided. The formula requires the means, standard deviations, and sample sizes for both samples. Since the standard deviations of the populations are not given, we would normally calculate the sample standard deviations for both the red and blue box data from the survey responses. However, the data needed to perform this calculation has not been provided in the question.

After obtaining the sample means and sample standard deviations, we would then apply the formula for the standard deviation of the difference between two means:

SD_difference = sqrt((SD_red^2 / n_red) + (SD_blue^2 / n_blue))

Where SD_red and SD_blue are the sample standard deviations, and n_red and n_blue are the sample sizes for red and blue boxes, respectively. This calculation would yield the standard deviation of the mean differences, which can then be used to perform a hypothesis test to assess the significance of the differences between the two packaging color options.