In: Statistics and Probability
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.
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.