Question: A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample are given below:
Hypothesized Difference 0
Level of Significance 0.05
Population Sample 1:
Sample Size 18
Sample Mean 48266
Sample Standard Deviation 13577
Population Sample 2:
Sample Size 12
Sample Mean 55000
Sample Standard Deviation 11741
Difference in Sample Means -6733
t-Test Statistic -1.40193
Lower-Tail Test:
Lower Critical Value -1.70113
P-Value 0.085962
(a) Referring to the table above, the researcher was attempting to show statistically that the female MBA graduates have a significant lower mean starting salary than the male MBA graduates. According to the test run, which is an appropriate alternative hypothesis?
(i) Hi : U females> U males
(ii) Hi : U females < U males
(iii) Hi : U females not equal U males
(iv) Hi : U females = U males
(b) Referring to the above table, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. From the analysis above, the correct test statistic is?
(i) 0.0860
(ii) -1.4019
(iii) -1.7011
(iv) -6733
(c) Referring to the table above, the researcher was attempting to show statistically that the female MBA graduates have a significant lower mean starting salary than the male MBA graduates. The proper conclusion for the test is?
(i) At the alpha-0.10 level, there is sufficient evidence to indicate difference in the mean starting salaries of male and female MBA graduates.
(ii) At the alpha-0.10 level, there is sufficient evidence to indicate that females have a lower mean starting salary than male MBA graduates.
(iii) At the alpha-0.10 level, there is sufficient evidence to indicate that females have a higher mean starting salary than male MBA graduates.
(iv) At the alpha-0.10 level, there is insufficient evidence to indicate any difference in the mean starting salaries of male and female MBA graduates.
(d) Referring to the table above, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. What assumptions were necessary to conduct this hypothesis test?
(i) Both populations of salaries (male and female) must have approximate normal distributions.
(ii) The population variances are approximately equal.
(iii) The samples were randomly and independently selected.
(iv) All of the above assumptions were necessary.
(e) Referring to the table above, what is the 99% confidence interval estimate for the difference between the two means?
(f) Referring to the table above, what is the 95% confidence interval estimate for the difference between the two means?