Question

.The Bureau of Labor Statistics reported that the average yearly income of dentists in the year 2010 was $110,000. A sample of 81 dentists, which was taken in 2011, showed an average yearly income of $120,000. Assume the standard deviation of the population of dentists’ incomes in 2011 is $36,000. a. We want to test to determine if there has been a significant increase in the average yearly income of dentists. Provide the null and the alternative hypotheses. ( please type the answer instead of writing it on paper )

Answer 1

Null and alternative hypotheses

Ho : = 110000

H1 : > 110000

Test statistic Z = (xbar - )/(/√n)

Z = ( 120000-110000)/(36000/√81)

Z = 2.50

Zcritical for a = 0.05 and right tailed test

Zcritical = Z​​​​​​1-a​​​ = Z​​​​​​0.95

Zcritical = 1.645

Decision rule : if Z > 1.645 we reject the null hypothesis otherwise we fail to reject the null hypothesis

Our Z = 2.50 > 1.645

Decision : we reject the null hypothesis Ho

Conclusion : There is sufficient evidence to support claim increase in the average yearly income of dentists.