Chapter 7, Problem 113E

To determine

To find: The mean, standard deviation and standard error of the mean of scores of four roommates and to determine whether it is correct to calculate the confidence interval for the data or not.

Answer to Problem 113E

Solution: The mean, standard deviation and standard error of the meanis 139.50, 15.02 and 7.51.As the data cannot be considered as simple random sampling, the confidence interval should not be calculated for this data.

Explanation of Solution

Calculation:

To obtain the mean, follow the steps below in Minitab software.

Step 1: Enter the data in the Minitab worksheet.

Step 2: Go to Stat and select the basic statistics, and then click on display the descriptive statistics.

Step 3: Enter the variable in the variables column.

Step 4: Choose the options as mean.

Step 5: Click on OK two times.

The mean is obtained as 139.50.

To obtain the standard deviation, follow the steps below in Minitab software.

Step 1: Enter the data in the Minitab worksheet.

Step 2: Go to Stat and select the basic statistics, and then click on display the descriptive statistics.

Step 3: Enter the variable in the variables column.

Step 4: Choose the options as mean.

Step 5: Click OK twice.

The standard deviation is obtained as 15.02.

To obtain the standard error, follow the steps below in Minitab software.

Step 1: Enter the data in the Minitab worksheet.

Step 2: Go to Stat and select the basic statistics, and then click on display the descriptive statistics.

Step 3: Enter the variable in the variables column.

Step 4: Choose the options as mean.

Step 5: Click OK twice.

The standard error is obtained as 7.51.

Interpretation: To compute the confidence interval for any dataset, the data should belong to simple random sampling. In the provided case, the data cannot be considered as simple random sampling because of the small sample size. Therefore, it is not appropriate if the confidence interval is calculated on the basis of the provided data.