Question

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. ��m1 - ��m2 = ��1��/n1 + ��2��/n2. In this formula, the subscripts m1 and m2 represent the means of the two samples, ��1 and ��2 are the standard deviations of the two populations, and n1 and n2 are the sample sizes.

Answer 1

To find out whether there's any difference in the mean number of people who would buy the new macaroni product, l-bow roni, with a red box and a blue box, you need to calculate the standard deviation of the sample mean differences using the formula:
`\(\sqrt{((\sigma_1^2 / n_1) + (\sigma_2^2 / n_2))/(2)}\)`.

Step-by-step explanation:

In the provided formula,
`\(\sigma_1\)` and
`\(\sigma_2\)` represent the standard deviations of the two populations, and
`\(n_1\)` and
`\(n_2\)` are the sample sizes. Given that you conducted 45 sessions with the red box (let's denote this as Sample 1) and 60 sessions with the blue box (denote this as Sample 2), you have the necessary values. For Sample 1,
`\(n_1 = 45\)` sessions, and for Sample 2,
`\(n_2 = 60\)` sessions. To find the standard deviation of the sample mean differences, you also need the standard deviations of the two populations
`\(\sigma_1\)` and
`\(\sigma_2\))`.

Ensure you have the individual data points for each session in each sample and calculate the sample standard deviations
`\(\sigma_1\)` and
`\(\sigma_2\))`. Substitute these values along with the sample sizes into the formula to obtain the standard deviation of the sample mean differences.

This standard deviation will help you assess whether the difference in the mean number of people willing to buy the product in red and blue boxes is statistically significant or just due to random variability. If the standard deviation is large, it suggests a more significant difference between the two samples.