Question

In: Statistics and Probability

In another study conducted in the same year (2015), the average monthly salary of residents in...

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?

Solutions

Expert Solution

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.

orchestra answered 1 year ago
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