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wrote...
Posts: 204
2 weeks ago
A random sample of 13 men and 19 women in a college class reported their grade point averages (GPAs). Here are histograms from the data:

Summary statistics for these data are:


A woman in the class says that she believes that college women tend to have higher GPAs than do college men. Does this sample support her claim? Test an appropriate hypothesis and state your conclusion.
Textbook 

Stats: Modeling the World


Edition: 4th
Authors:
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Answer verified by a subject expert
wrote...
Posts: 266
Rep: 6 0
2 weeks ago
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H0: μW - μM = 0, HA: μW - μM > 0  where M = men and W = women
* Independent group assumption: Men and women are definitely independent groups.
* Randomization condition: We are told that these are random samples of men and women in the class.
* 10% condition: These samples represents less than 10% of all possible men and less than 10% of all possible women taking the course.
* Nearly Normal condition: The samples are pretty small, but the histograms given don't seem to deviate too badly from being unimodal and symmetric.

Because the conditions are satisfied, it is appropriate to model the sampling distribution of the
difference in the means with a Student's t-model, and we will perform a two-sample t-test.
We know: nW = 19 W = 3.330 sW = 0.395
nM = 13 M = 2.898 sM = 0.583
SE(W - M) = = = = = 0.185
The observed difference is W - M = 3.330 - 2.898 = 0.432.
t = = = 2.335
The sampling distribution model has 19.44 degrees of freedom.
P(t19.44 > 2.335) = 0.0152.

This P-value is low, so we reject the null hypothesis. There is evidence that college women have a higher mean GPA than do college men.
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wrote...
2 weeks ago
A random sample of 13 men and 19 women in a college class reported their grade point averages (GPAs). Here are histograms from the data:

Summary statistics for these data are:


Create and interpret a 95% confidence interval.
wrote...
2 weeks ago
We wish to create an interval that is likely to contain the true difference between the mean GPAs of
college women and college men.

The conditions were satisfied above, so the sampling model of the difference in the sample means can be modeled by a Student's t-model with about 19 degrees of freedom (from calculator). We will use a two-sample t-interval.
The 95% confidence interval is: (0.045, 0.819).
We are 95% confident that the mean GPA for college women is 0.045 to 0.819 points higher than the
mean GPA for college men..
wrote...
2 weeks ago
Thanks
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