Question

1. The Bureau of Labor Statistics reported that the average yearly income of dentists in the year 2009 was $116,000. Dr. Smith thinks there has been a significant increase in the average yearly income of dentists. He has a dataset of a sample of 81 dentists, which was taken in 2010, showed an average yearly income of $123,000. Assume the standard deviation of the population of dentists in 2010 is $36,000. Please answer the following questions:

(a)	Develop appropriate null and alternative hypotheses such that rejection of H0 will support Dr. Smith’s argument.
(b)	Compute the test statistic.
(c)	Determine the p-value; and at 95% confidence, test the hypotheses.

[Hint: This is a One-tailed Hypothesis Testing.

If it can be typed I would highly appreciate it so I can understand and read it better.

Answer 1

x̅ =   123000, σ =   36000, n =   81
α =    0.05

a) Null and Alternative hypothesis:  
Ho : µ =   116000
H1 : µ >   116000

b) Test statistic:  
z = (x̅- µ)/(σ/√n) = 1.75

c) p-value = 1- NORM.S.DIST(1.75, 1 ) = 0.0401

Decision: p-value <alpha, so we reject the null hypothesis.

There is enough evidence to conclude that there has been a significant increase in the average yearly income of dentists at 0.05 significance level.