Question

Employees at a construction and mining company claim that the mean salary of the company’s mechanical engineers is less than that of the one of its competitors, which is $68,000. A random sample of 30 of the company’s mechanical engineers has a mean salary of $66,900 with a standard deviation of $5500. At
α = 0.05, test the employees’ claim.

Answer 1

Null and alternative hypotheses

Ho : = 68000

Ha : < 68000

Level of significance a = 0.05

Test statistic

t = ( xbar - )/(s/√n)

Where n = 30 , xbar = 66900 , s = 5500

t = (66900 - 68000)/(5500/√30)

t test statistic = -1.10

t critical value for a = 0.05 , d.f = n -1 = 29

tCritical = t​​​​​​ a , n-1 = t​​​​​​0.05, 29

tCritical = -1.70

Decision rule : if t < -1.70 , we reject the null hypothesis otherwise we fail to reject the null hypothesis

Our t = -1.10 > -1.70

Conclusion : Fail to reject the null hypothesis Ho . There is no sufficient evidence to support the claim thatthe mean salary of the company’s mechanical engineers is less than that of the one of its competitors, which is $68,000