Question

task 3
sample mean differences and standard deviation
as a member of the marketing team for a pasta manufacturer, you want to find out whether theres 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 competitors 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, youll use this formula for the standard deviation of sample mean differences.
$sigma_{m_1}-sigma_{m_2}=sqrt{\frac{sigma_1^2}{n_1}+\frac{sigma_2^2}{n_2}}$
in this formula, the subscripts $m_1$ and $m_2$ represent the means of the two samples, $sigma_1$ and $sigma_2$ are the standard deviations of the two populations, and $n_1$ and $n_2$ are the sample sizes.
part a
question
use the spreadsheets 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

Explanation:

Step1: Open the spreadsheet

Locate the data for red - box sessions and blue - box sessions.

Step2: Use the Average function

For the red - box data (45 sessions with 30 people per session), use the spreadsheet's Average function under AutoSum in the Function menu. Let the number of yes - responses in each of the 45 sessions be \(x_1,x_2,\cdots,x_{45}\). The mean \(M_1=\frac{\sum_{i = 1}^{45}x_i}{45}\), round to the nearest hundredth.

Step3: Use the Average function for blue - box data

For the blue - box data (60 sessions with 30 people per session), let the number of yes - responses in each of the 60 sessions be \(y_1,y_2,\cdots,y_{60}\). The mean \(M_2=\frac{\sum_{i = 1}^{60}y_i}{60}\), round to the nearest hundredth.

Since the actual data values from the data sheet are not provided, we cannot calculate the exact numerical values. But the general steps for calculation are as above.

Answer:

The mean value of people who would purchase the red box: [Value calculated using the spreadsheet's Average function and rounded to nearest hundredth]
The mean value of people who would purchase the blue box: [Value calculated using the spreadsheet's Average function and rounded to nearest hundredth]