Question

Difference in means test

Continuing the previous question, suppose you take a sample of 560 males and 570 females at Mencion and record their salaries. The males have an average salary of $70,982 with a standard deviation of $6,272, and the females have an average salary of $69,742 with a standard deviation of $9,593

What is the P-value for the following hypothesis test?

H0: μ1 = μ2
H1: μ1 < μ2

Report your answer as a decimal (between 0 and 1) rounded to three (3) decimal places

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ALSO:

According to your answer above, is there significant evidence that women are paid less than men at this company?

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Answer 1

Given that,

For Female :

For males :

The null and alternative hypotheses are,

H0 : μ1 = μ2

H1 : μ1 < μ2

Test statistic is,

=> Test statistic = Z = -2.58

p-value = P(Z < -2.58) = 0.0049

=> p-value = 0.005

Since, p-value = 0.005 < 0.05, we reject the null hypothesis.

Conclusion : There is significant evidence that women are paid less than men at this company.