Question

Columbia College advertises that the mean starting salary of its graduates is $39,000. The committee for Truth in Advertising, an independent organization, suspect that this claim is exaggerated and decides to conduct a hypothesis test to seek evidence to support its suspicious. A random sample of 100 graduates is used and the mean salary of the sample is $37,000, standard deviation of sample is $6,150. Use a 0.05 level of significance. Find also the p-value.

Answer 1

Solution :

Given that,

Population mean = = 39000

Sample mean = = 37000

Sample standard deviation = s = 6150

Sample size = n = 100

Level of significance = = 0.05

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 39000

Ha: 39000

The test statistics,

t = ( - )/ (s/)

= ( 37000 - 39000) / ( 6150/100)

= -3.252

p-value:

df = n - 1 = 99

p-value = 0.0016

The p-value is p = 0.0016 < 0.005, it is concluded that the null hypothesis is rejected.

Conclusion:

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean

μ is different than 39000, at the 0.05 significance level.