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Hypothesis Testing for Graded Assignment

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Use the Student_Data.xls file to solve the following. For each problem, be sure to state the direction of the test used, the decision to reject the null or not, and the conclusion in English.:

Problem 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.

Problem 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 sub-par 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.

Problem 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.

Problem 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.

NOTE: You can either copy your output into Word and include findings with your output OR you can type your findings directly onto the Excel spreadsheet, but make sure that what you write is easy to find.

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Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis. Formula for the calculation and Interpretations of the results are also included.

Solution Preview

Problem 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.
Answer
We can determine whether the mean GPA differs for men and women using "Independent sample t test assuming equal variances." Since no specific direction is mentioned in the problem, a two-tailed test is appropriate here.
The Null hypothesis tested is
H0: There is no significant difference in the mean GPA for men and women. (µ1= µ2)
The Alternative hypothesis is
H1: There is significant difference in the mean GPA for men and women. (µ1≠ µ2)
The Test statistic used is
Where
Here = 3.423586957, = 3.6025, S1 = 0.272931105, S2 = 0.264805077, n1 = 92, n2 = 108
Now = 0.268570301
Therefore, = -4.695423954
Rejection criteria: Reject the null hypothesis, if the absolute value of calculated t is greater than the critical value of t at the 0.05 significance level.
Critical values = ±1.972017432
Conclusion: Reject the null hypothesis, since the absolute value of calculated t is greater than the critical value of t. The sample provides enough evidence to support the claim that there is significant difference in the mean GPA between men and women. Hence we can conclude that the mean GPA differs for men and women.
Details
Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference 0
Level of Significance 0.05
Male
Sample Size 92
Sample Mean 3.423586957
Sample Standard Deviation 0.272931105
Female
Sample Size 108
Sample Mean 3.6025
Sample Standard Deviation 0.264805077

Intermediate Calculations
Population 1 Sample Degrees of Freedom 91
Population 2 Sample Degrees of Freedom 107
Total Degrees of Freedom 198
Pooled Variance 0.072130007
Standard Error 0.0381
Difference in Sample ...

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