Question

I need help on question 3!

Problem 2: salaries of lawyers and doctors, mean edition An experiment is conducted to determine whether the mean salary for doctors and lawyers is the same. 13 doctors are sampled IID and their salaries are assumed to come from a normal distribution. 11 lawyers are sampled IID and their salaries are assumed to also come from a normal distribution. For time being, assume the variances in salary are the same for the doctor and lawyer populations. The sample average salary for doctors is 120000 with a sample standard deviation of 5000 dollars, whereas the sample average salary for lawyers is 90000 with a sample standard deviation of 15000 dollars. Conduct a size .01 test to determine whether the population mean for lawyer salaries is equal to that of doctor salaries. Clearly write out the null, alternative, and type of hypothesis test that you are conducting.

Answer 1

Problem 3:

H0: Null Hypothesis: (The variance of lawyer salaries does not exceed that of doctor salaries)

01 <024

HA: Alternative Hypothesis: (The variance of lawyer salaries exceeds that of doctor salaries) (claim)

01² > 024

Lawyer:

n1 = 11

$\bar{x}$1 = 90,000

s1 = 15,000

Doctor:

n2 = 13

$\bar{x}$2 = 120,000

s2 = 5,000

Test Statistic is given by:

$F=\frac{s1^{2}}{s2^{2}}=\frac{15,000^{2}}{5,000^{2}}=9.00$

$\alpha$ = 0.05

Degrees of Freedom for numerator = 11 - 1 = 10

Degrees of Freedom for denominator = 13 - 1 = 12

One Tail - Right Side Test

By Technology, critical Value of F = 2.753

Since calculated value of F = 9.00 is greater than critical value of F = 2.753, the difference is significant. Reject null hypothesis.

Conclusion:

The data support the claim that the variance of lawyer salaries exceeds that of doctor salaries.