Question

In another study conducted in the same year (2015), the average monthly salary of residents in Bordeaux was found to be about €2353. And the standard deviation of the monthly salaries was €420.

In 2017, a study on the salary distribution of Paris residents was conducted. Assume that the salaries were normally distributed. A random sample of 10 salaries was selected and the data are listed below:

3200 3500 3000 2100 2950 2050 2440 3100 3500 2500

Question 8:

Assume that the standard deviation of the salaries was still the same as in 2015. Estimate the average salary (in 2017) with 95% confidence.

Question 9:

The assumption made in Question 8 was certainly unrealistic. Estimate the average salary (in 2017) with 95% confidence again assuming that the standard deviation had changed from 2015.

Question 10:

Estimate the variance of monthly salaries of Paris residents (in 2017) based on the sample provided above at a 95% confidence level.

Question 11:

How would you interpret the result in Question 10 above?

Answer 1

Solution: The mean and standard deviation of the given data is:

Question 8:

Assume that the standard deviation of the salaries was still the same as in 2015. Estimate the average salary (in 2017) with 95% confidence

Answer: The 95% confidence interval is:

Where:

is the critical value at 0.05 significance level

Therefore, we have:

Question 9:

The assumption made in Question 8 was certainly unrealistic. Estimate the average salary (in 2017) with 95% confidence again assuming that the standard deviation had changed from 2015.

Answer: The 95% confidence interval is:

Where:

is the critical value at 0.05 significance level for degrees of freedom = n - 1 = 9

Therefore, we have:

Question 10:

Estimate the variance of monthly salaries of Paris residents (in 2017) based on the sample provided above at a 95% confidence level.

Answer: The 95% confidence interval estimate for the population variance is:

Where:

Therefore, we have:

Question 11:

How would you interpret the result in Question 10 above?

Answer: There is a 95% chance that the confidence interval calculated contains the true value of the population variance.