Question

According to the Chronicle of Higher Education, the average number of applications for an assistant professor position in US universities is 59.8, with a standard deviation of 13.6. A

researcher thinks that the average number is actually less than 59.8, and his sample of 100

advertised positions at US universities produced a mean of 56.2 applicants. Test his claim, using

a significance level of .05. Show all the steps (4 steps) discussed in the lecture video.

Answer 1

Solution:

Population SD = 13.6

Claim : average number is actually less than 59.8

1)

The null and alternative hypothesis are

H0 : =  59.8

H1 :   < 59.8

2)

The test statistic z is given by

z =

= (56.2 - 59.8) / (13.6/100)

= -2.65

Test statistic z = -2.65

3)

Now , observe that ,there is < sign in H1. So , the test is left tailed.

So ,

p value = P(Z < z) = P(Z < -2.65) = 0.0040

p value is 0.0040

4)

p value is less than given level of significance = 0.05

Reject H₀

We can conclude that there is sufficient evidence to support the claim that that the average number is actually less than 59.8.