Question

1) A university wants to know if the average salary of its graduates has increased since 2015. The average salary of graduates prior to 2015 was $48,000. Since 2015, the university surveyed 256 graduates and found an average salary of $48,750. Assume that the standard deviation of all graduates' salaries is $7,000.

b. Calculate the value of the test statistic and the p-value at a 5% significance level.

c. At the 5% significance level, can you conclude that salaries, on average, have increased? Explain.     

Answer 1

Solution:

a)

The null and alternative hypothesis are

H0 : = 48000

Ha : > 48000

b)

Test statistic z = = [48750 - 48000]/[7000/256] = 1.71

Test statistic z = 1.71

Right tailed test here .

p value = P(Z > z) = P(Z > 1.71) = 1 - P(Z < 1.71) = 1 - 0.9564 = 0.0436

p value = 0.0436

c)

We  reject the null hypothesis

(Because p value is less than the level of significance 0.05 )

Yes , we can conclude that salaries, on average, have increased .