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?

Answer 1

1) Ha :   µ >   2200

2) population std dev ,    σ =    550.0000                  
Sample Size ,   n =    64                  
Sample Mean,    x̅ =   2385.0000                  
                          
'   '   '                  
                          
Standard Error , SE = σ/√n =   550.0000   / √    64   =   68.7500      
Z-test statistic= (x̅ - µ )/SE = (   2385.000   -   2200   ) /    68.7500   =   2.691

3)

critical z value, z* =       1.645

reject ho if z >1.645

4)

p-Value   =   0.0036

5) Decision:   p-value<α, Reject null hypothesis   
Conclusion: There is enough evidence to conclude that the average salary had increased