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wrote...
Posts: 228
3 weeks ago
A total of 23 Gossett High School students were admitted to State University. Of those students, 7 were offered athletic scholarships. The school's guidance counselor looked at their composite ACT scores (shown in the table), wondering if State U. might admit people with lower scores if they also were athletes. Assuming that this group of students is representative of students throughout the state, what do you think?




Test an appropriate hypothesis and state your conclusion.
Textbook 

Stats: Modeling the World


Edition: 4th
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wrote...
Posts: 223
3 weeks ago
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Let: mean ACT score of non-athletes = μ1 and mean ACT score of athletes = μ2
H0: μ1 - μ2 = 0 , HA: μ1 - μ2 > 0
* Independent group assumption: Non-athletes and athletes are definitely independent groups.
* Randomization condition: These are not random samples, but they should be representative of athletes and nonathletes.
* 10% condition: The samples represent less than 10% of all possible non-athletes and less than 10% of all possible athletes who could be admitted to State U. from Gossett High School.
* Nearly Normal condition: The histograms show that both sets are unimodal and roughly 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.
n1 = 16 1 = 24.75 s1 = 2.84
n2 = 7 2 = 21.86 s2 = 3.29
SE(1 - 2) = = = = 1.432
The observed difference is 1 - 2 = 24.75 - 21.86 = 2.89
t = = = 2.02
The sampling distribution model has 10.13 degrees of freedom.

Since the P-value is low, we reject the null hypothesis. There is evidence of a difference between the mean ACT scores for non-athletes and athletes.
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wrote...
3 weeks ago
A total of 23 Gossett High School students were admitted to State University. Of those students, 7 were offered athletic scholarships. The school's guidance counselor looked at their composite ACT scores (shown in the table), wondering if State U. might admit people with lower scores if they also were athletes. Assuming that this group of students is representative of students throughout the state, what do you think?




Create and interpret a 90% confidence interval.
wrote...
3 weeks ago
We wish to create an interval that is likely to contain the true difference between the mean ACT score for non-athletes and athletes.
Under these conditions, the sampling model of the difference in the sample means can be modeled by a Student's t-model with about 10 degrees of freedom (from calculator).
We will use a two-sample t-interval.
The 90% confidence interval is: (0.30, 5.48).

We are 90% confident that non-athletes average between 0.30 points and 5.48 points higher than athletes on the ACT.
wrote...
3 weeks ago
I appreciate what you did here, answered it correctly Smiling Face with Open Mouth
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