Question

In a study of monthly salary distribution of residents in Paris conducted in year 2015, it was found that the salaries had an average of €2200 (EURO) and a standard deviation of €550. Assume that the salaries were normally distributed.

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 1: 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 2: 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 3: Estimate the variance of monthly salaries of Paris residents (in 2017) based on the sample provided above at a 95% confidence level.

A similar study was conducted on salary distribution of Paris residents in 2019. The research team aimed to estimate the average salary. They chose the 98% confidence and assumed that the population standard deviation was the same as in 2015. Assume again that those salaries were normally distributed.

Question 4 :If they would like the (margin of) error to be no more than €60, how large a sample would they need to select? (That is, find the minimum sample size.)

Select one:

A: 322

B: 323

C: 456

D: 457

Answer 1