Perform the indicated test. Assume that the two samples are independent simple r
ID: 3297102 • Letter: P
Question
Perform the indicated test. Assume that the two samples are independent simple random samples selected
from normally distributed populations. Also, do not assume that the population standard deviations are equal (1 2).
A researcher interested in comparing salaries of female and male employees at a particular company. Independent
random samples of 8 female and 15 male employees made the following weekly salaries.
Female: 495, 760, 556, 904, 520, 1005, 743, 660
Male: 722, 562, 880, 520, 500, 1250, 750, 1640, 518, 904, 1150, 805, 480, 970, 605
Use a 0.05 significance to test claim that mean female salary is less than the mean male salary. Use the traditional method of hypothesis testing.(Note:x-bar1= 705.375 ,x-bar 2=817.067, S1=183.885, S2 = 330.146
Explanation / Answer
Hypotheses: The null and alternative hypotheses are as follows:
H0:muF-muM=0 (there is no difference in mean salaries for female and male)
H1:muF-muM<0 (mean female salary is less than mean male salary)
Assumptions: Independent groups assumption: Randomizing the experiment gives independent groups. Independence assumption: the salaries in each group has been drawn independently and at random. Normal population assumption: the randomly drawn samples come from normally distributed populations.
The assumptions are reasonably met, and the conditions are satisfied, use Student's t model to perform two-sample t test.
From given data, xbarF=705.375, sF=183.885, nF=8, xbarM=817.067, sM=330.146,nM=15
t=(xbarF-xbarM)/sqrt[s^2F/nF+s^2M/nM]
=(705.375-817.067)/sqrt[183.885^2/8+330.146^2/15]
=-1.04
df=[{s^2F/nF+s^2M/nM}^2/{1/nF-1(s^2F/nF)^2+1/nM-1(s^2M/nM)^2}]
Substituting the values, the degres of freedom (rounded) is 20.
P value at 20 df is 0.155.
Rejection rule: Reject null hypothesis if P value is less than alpha=0.05. Here, P value is not less than 0.05. Therefore, fail to reject null ypothesis.
Conclusion: There is insufficient sample evidence to support the claim that mean female salary is less than mean male salary.