Part 1. Single Mean Tests (Chapter 8) 1) A group of 17 male prisoners in federal
ID: 3227860 • Letter: P
Question
Part 1. Single Mean Tests (Chapter 8)
1) A group of 17 male prisoners in federal, maximum-security penitentiaries was randomly selected from a federal prison population to participate in a new rehabilitation program. The 17 prisoners had a mean score on a “dangerousness to society” index (low score = not dangerous, high score = extremely dangerous) of 84 and a standard deviation of 16. The federal prison population mean index score is µ = 90. Is there evidence that the rehabilitation program works?
Follow the 5-step model for hypothesis testing when writing your answer; you can set the alpha level as =0.05.
2) A professor gives the class an examination that, as he knows from years of experience, yields a µ = 75. The present class of 22 students obtains and s = 7. Is the professor correct in inferring that this class represents a “superior” population of students?
Follow the 5-step model for hypothesis testing when writing your answer; you can set the alpha level as =0.01.
3) As the president of UAardvark, you are considering a policy making an English composition class required for all first-year graduate students. You will implement this policy if you find evidence that your current graduate students’ average verbal GRE score is lower than the national average verbal GRE score (u= 443) at the .05 level of significance ( ). You have a random sample (N) of 70 graduate students. Your students’ average verbal GRE score (x) is 435 with a standard deviation (s) of 35.
Use our five-step model for hypothesis testing to answer the question “Does UAardvark adopt the new policy?”
Part 2. A Difference in Means Test (Chapter 9)
1) A random sample of 75 female students at an all-women's college scored a mean of 84 with a standard deviation of 5 on a standardized exam, while a random sample of 50 female students at a large coed university scored an average of 80 with a standard deviation of 4 on this exam. Your research hypothesis is that all-women schools have superior learning environments for their female students.
Follow the 5-step model for hypothesis testing when writing your answer; you can set the alpha level as =0.05.
https://blackboard.albany.edu/bbcswebdav/pid-2704609-dt-content-rid-13137478_1/courses/2173-ASOC-221-6872/Five%20step%20model%20of%20hypothesis%20testing.pdf
Explanation / Answer
(1)
Data:
n = 17
= 90
s = 16
x-bar = 84
Hypotheses:
Ho: 90
Ha: < 90
Decision Rule:
= 0.05
Degrees of freedom = 17 - 1 = 16
Critical t- score = -1.745883669
Reject Ho if t < -1.745883669
Test Statistic:
SE = s/n = 16/17 = 3.880570001
t = (x-bar - )/SE = (84 - 90)/3.88057000058133 = -1.54616461
p- value = 0.070806813
Decision (in terms of the hypotheses):
Since -1.54616461 > -1.745883669 we fail to reject Ho
Conclusion (in terms of the problem):
There is no sufficient evidence that the rehabilitation programme works.