A researcher randomly sampled 30 graduates of an MBA program and recorded data c

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 is given below. Referring to Table 10-2, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. The proper conclusion for this test is: At the alpha = 0.10 level, there is sufficient evidence to indicate a difference in the mean starting salaries of male and female MBA graduates. At the alpha = 0.10 level, there is sufficient evidence to indicate that females have a lower mean starting salary than male MBA graduates. At the alpha = 0.10 level, there is sufficient evidence to indicate that females have a higher mean starting salary than male MBA graduates. 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.

Explanation / Answer

Solution:-

11) b) At alpha = 0.10 level, There is sufficient evidence to indicate that females have a lower mean starting salary than male MBA graduates.

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: Female = Male

Alternative hypothesis: Female < Male

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the mean difference between sample means is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.10. Using sample data, we will conduct a two-sample t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

t = [ (x1 - x2) - d ] / SE

t = - 1.40

where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.

P(t < - 1.40) = 0.086

Interpret results. Since the P-value (0.086) is less than the significance level (0.10), we have to reject the null hypothesis.

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