In: Statistics and Probability
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 |
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.
a. 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 , Answer )
b. The assumption made in Question a was certainly unrealistic. Estimate the average salary (in 2017) with 95% confidence again assuming that the standard deviation had changed from 2015.
( Answer , Answer )
c. Estimate the variance of monthly salaries of Paris residents (in 2017) based on the sample provided above at a 95% confidence level.
( Answer , Answer )
d.
How would you interpret the result in Question c above?
Select one:
We are 95% confident that the confidence interval obtained in Question 10 contains s2s2.
We are 95% confident that the confidence interval obtained in Question 10 contains σ2σ2.
We are 90% confident that the confidence interval obtained in Question 10 contains σ2σ2.
We are 95% confident that the confidence interval obtained in Question 10 contains μμ.
We are 95% confident that the confidence interval obtained in Question 10 contains x¯¯¯x¯.
We are 90% confident that the confidence interval obtained in Question 10 contains μμ.