In: Statistics and Probability
The Bureau of Labor Statistics reported that the average yearly income of dentists in the year 2012 was $110,000. A sample of 81 dentists, which was taken in 2013, showed an average yearly income of $120,000. Assume the standard deviation of the population of dentists’ incomes in 2013 is $36,000.
Test the hypotheses at 95% confidence. |
Given:
= 110000,
= 120000,
= 36000, n = 81,
= 0.05
The Hypothesis:
H0:
= 110,000
Ha:
110,000
This is a 2 tailed test
The Test Statistic: Since the population standard deviation is known, we use the z test.
The test statistic is given by the equation:
The p Value: The p value (2 Tail) for Z= 2.5, is; p value = 0.0124
The Critical
Value: The critical value (2 Tail) at
= 0.05, Zcritical= +1.96 and - 1.96
The Decision Rule: If Zobservedis > Zcritical or if Zobserved is < -Zcritical, Then reject H0.
Also if P value is <
, Then Reject H0.
The Decision: Since Zobserved (2.5) is > Zcritical (1.96), We Reject H0.
Also since P value (0.0124) is <
(0.05) , We Fail to Reject H0.
The Conclusion: There is sufficient evidence at the 95% significance level to warrant rejection of the claim that the average yearly income of dentists in the year 2012 was equal to $110,000.