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. (Answer up to 4^th decimal points for each numerical question.)

Question 1:

Set up the alternative hypothesis.

Select one:

x¯¯¯>2200x¯>2200

μ>2200μ>2200

μ>2385μ>2385

x¯¯¯>2385

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.

Select one:

z>1.645z>1.645

z<−1.645z<−1.645

z>1.96z>1.96

z<−1.96z<−1.96

z>2.33z>2.33

z<−2.33

Question 4: Based on the assumption in Question 2, find the pp-value.

Question 5: What is the conclusion?

Select one:

There is not enough evidence to infer that the average salary had increased at 5% significance level.

There is enough evidence to infer that the average salary had increased at 5% significance level.

There is enough evidence to infer that the average salary had increased at 10% significance level.

There is not enough evidence to infer that the average salary had increased at 10% significance level.

There is enough evidence to infer that the average salary had increased at 2.5% significance level.

Question 6: The assumption made in Question 2 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.

Select one:

t>1.6706t>1.6706

t>1.6686t>1.6686

t>1.9971t>1.9971

t>2.0003

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 tt-test to test the suspicion. But they had no information on the two population variances. So they first conducted an FF-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=1= Paris;  2=2= Bordeaux.

Question 8: Set up the alternative hypothesis for the FF-test.

Question 9: In the FF-test, what is the test statistic? Find the rejection region in the FF-test.

Question 10:What is the conclusion?

Select one:

There is enough evidence to infer that H1H1 is true.

There is not enough evidence to infer that H1H1 is true

Question 11: The analyst then conducted an appropriate tt-test at a significance level of 5% to test the suspicion. Set up the alternative hypotheses for the tt-test.

Question 12: Find the test statistic in the tt-test and the rejection region in the tt-test.

Question 13: What is the conclusion?

Select one:

There is enough evidence to infer that μ1μ1 is lower than μ2μ2 at 5% significance level.

There is not enough evidence to infer that μ1μ1 is lower than μ2μ2 at 5% significance level.

There is not enough evidence to infer that x¯¯¯1x¯1 is lower than x¯¯¯2x¯2 at 5% significance level.

There is enough evidence to infer that x¯¯¯1x¯1 is lower than x¯¯¯2x¯2 at 5% significance level.

There is enough evidence to infer that x¯¯¯1x¯1 is lower than x¯¯¯2x¯2 at 2.5% significance level.

Answer 1