Question

It is stated that the average wage for a particular profession is $60K however a researcher believes that the actual wage of this profession is less. A random sample of N = 30 individuals working in this profession are taken and it is found that the sample mean is $57K and a sample standard deviation of $8K. Test this hypothesis at the 1% significance level.

Reject the null

Fail to Reject

Answer 1

Solution :

Given that,

Population mean = = 60

Sample mean = = 57

Sample standard deviation = s = 8

Sample size = n = 30

Level of significance = = 0.01

This is a left (One) tailed test,

The null and alternative hypothesis is,  

Ho: 60

Ha: 60

The test statistics,

t = ( - )/ (s/)

= ( 57 - 60 ) / ( 8 / 30 )

= -2.054

P-value = 0.0245

The p-value is p = 0.0245 > 0.01, it is concluded that the null hypothesis is fail to rejected.

Fail to Reject