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Significance Levels, Mean, Null and Alternative Hypothesis

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1. The battle of the sexes lives on still today. Since admission standards do not address gender whatsoever, there should be an equally diverse group of men and women in school, but do they perform equally well. Using the sample of 200 students, conduct a hypothesis test for two independent samples to determine if the mean GPA differs for men and women. Use a .05 significance level.

2. Can a student keep up their grade performance at the next level? Is a strong GPA at the Bachelors level a good predictor of a strong GPA at the Masters level, or are GPAs naturally going to decline since graduate school is tougher, or will GPAs automatically be higher in graduate school because of the 3.00 requirement to graduate and the treatment of a C as subpar instead of average? Using the sample of 200 students (in the data file), conduct a hypothesis test for paired samples and test if there is a difference in the mean GPA from the Bachelors to the Masters programs. Use a .05 significance level.

3. Given the reasons why people get their Masters, you surmise that men are more likely to declare a major than women. Using the sample of 200 students (in the data file), conduct a hypothesis test of proportions to determine if the proportion of women with "no major" is greater than the proportion of men with "no major". Use a .05 significance level.

4. You have probably heard that if you want something done, give it to a busy person. So is one's employment status a factor in their academic performance? Using the sample of 200 students (in the data file), conduct a hypothesis test using Analysis of Variance to determine if there is a difference in the mean GPA for those who are unemployed vs. work part-time vs. work full-time.

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The Solution uses basic statistics concepts to find the answer to the questions about significance, samples and finding hypotheses.

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1. The battle of the sexes lives on still today. Since admission standards do not address gender whatsoever, there should be an equally diverse group of men and women in school, but do they perform equally well. Using the sample of 200 students, conduct a hypothesis test for two independent samples to determine if the mean GPA differs for men and women. Use a .05 significance level.

Null Hypothesis (Ho): There is no significant difference in the population mean GPA between men and women i.e. µ1 = µ2

Alternative Hypothesis (Ha): There is a significant difference in the population mean GPA between men and women i.e. µ1 ≠ µ2.

where µ1 is the population mean GPA of men and µ2 is the population mean GPA of women.

Since there are two GPAs provided in the sample one overall GPA in the BS program and other is overall GPA in the MBA program, so we will perform two analyses on this and conclude based MBA and BS mean GPA.

MBA GPA analysis

Level of Significance 0.05

Female MBA_GPA Male MBA_GPA
Sample Mean 3.387 3.446
Sample Size 64 136
Sample Standard Deviation 0.372 0.342

Standard Error (Computed) 0.05
Test Statistic (Computed) -1.08

Conclusion:
We can see that the test statistic is -1.08 which lies between -1.96 and 1.96 lower and upper critical values so we will not be able to reject Ho and conclude that there is no significant difference in the population mean MBA GPA between men and women i.e. µ1 = µ2.

BS GPA analysis
Level of Significance 0.05

Female BS_GPA Male BS_GPA
Sample Mean 3.535 3.541
Sample Size 64 136
Sample Standard Deviation 0.329 0.315

Standard Error (Computed) 0.05
Test Statistic (Computed) -0.12

Conclusion:
We can see that the test statistic is -0.12 which lies between -1.96 and 1.96 lower and upper critical values so we will not be able to reject Ho and conclude that there is no significant difference in the population mean BS GPA between men and women i.e. µ1 = µ2.

So based on the above analysis we can conclude that mean GPA do not differs for men and women.

2. Can a ...

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