A politician claims that the mean salary for managers in his state is more than national mean $82,000.  The salaries (in dollars) for a random sample of 30 managers in the state are listed. At α = 0.07, is there enough evidence to support the claim?

Solution:

a) Identification of Null and alternative hypotheses:

Null hypothesis:

H₀ The mean salary for managers in the state is not more than $82000

H₀  µ ≤ 82000

alternative hypothesis:

H₀  The mean salary for managers in the state is more than $82000

H₀  µ > 82000

Level of significance (α) = 0.07                         One tailed test

Assumptions:

Population is normally distributed.

Data Information: In the above data we find

n (Sample size) =  30

σ (Population standard deviation)   = 8315.90

 X‾ (Sample mean) = 83410.97

b) Calculation of Test Statistic:

c) Finding P value

P value   = P (Z > Z observed)

             = P (Z > 0.93)

             = 1 - P(Z < 0.93)

             = 1- 0.8238

             = 0.1762   

d) Decision Rule:

 Reject H₀ if P value is less than the level of significance.

Decision:

Since P value (observed level of significance) = 0.1762 is greater than α (level of significance) = 0.07, we fail to reject H₀.