Question

26. Teachers’ salaries are so low in a state that administrators have to constantly defend their own numbers. The state claims that the mean salary is $ 33,600. A group of citizens randomly select files of 22 teachers in the area and find that the mean salary is $32,400, with a standard deviation of $1520. Test the administrators’ claim at the 0.01 significance level. Assume normality.

a)

b)

c)

D)

E)

Answer 1

Solution :

Given that,

a)

The null and alternative hypothesis is,

Ho: 33600

Ha: 33600

b)

This is a two tailed test.

c)

The test statistics,

t =( - )/ (s /n)

= ( 32400 - 33600 ) / ( 1520 / 22 )

= -3.703

d)

P- Value = 0.0013    

The p-value is p = 0.0013 < 0.01, it is concluded that the null hypothesis is rejected.

e)

Conclusion :

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the mean salary is different than $ 33,600, at the 0.01 significance level.