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.

One years later (in 2016), it was suspected that the average salary had increased. A hypothesis test was conducted at a significance level of 5% to test the suspicion. A random sample of size 64 was chosen with mean of €2385 and standard deviation of €650.

Question 1:

Set up the alternative hypothesis.

Question 2:

Assume that the population standard deviation had not changed from 2015. Find the test statistic.

Question 3:
Based on the assumption in Question 2 above, find the rejection region.

Question 4:

Based on the assumption in Question 2, find the p-value.

Question 5:

What is the conclusion?

Question 6:

The assumption made in Question 1 was certainly not reasonable. Find the test statistic again, assuming that the population standard deviation had changed from 2015. Also assume that the population was normal.

Question 7:

Find the rejection region again based on the new assumptions made in Question 6.

In another study conducted in 2016, the average of monthly salaries of 45 randomly chosen residents in Bordeaux was found to be €3200; the sample standard deviation of the chosen salaries was €600. The suspicion was that the average salary of residents in Paris is lower than the average salary of residents in Bordeaux.

The research team was to conduct a ?-test to test the suspicion. But they had no information on the two population variances. So they first conducted an ?-test at a significance level of 5% to determine if the two population variances are equal or not, assuming that both populations were normal.

Set 1 = Paris; 2 = Bordeaux.

Question 8:

Set up the alternative hypothesis for the ?-test.

Question 9:

In the ?-test, what is the test statistic?

Question 10:

Find the rejection region in the ?-test.

Question 11:

What is the conclusion?

Question 12:

The analyst then conducted an appropriate ?-test at a significance level of 5% to test the suspicion. Set up the alternative hypotheses for the ?-test.

Question 13:

Find the test statistic in the ?-test.

Question 14:

Find the rejection region in the ?-test.

Question 15:

What is the conclusion?

Answer 1