Your answer is CORRECT. 10 points. DO NOT place the problem code on the answer s
ID: 3318698 • Letter: Y
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Your answer is CORRECT. 10 points. DO NOT place the problem code on the answer sheet. A submission. Show all steps (work) on your answer sheet for full This is a written question, worth 10 points. DON proctor will fill this out after exam submission, credit. Problem Code: 1561 Are urban students more successful? North Carolina success of students in a required chemical engineeri. course in order to continue as chemical engineering m suburban backgrounds, and 53 of these students succeede town backgrounds; 31 of these students succeeded in the North Carolina State University looked at the factors that affect the chemical engineering course. Students must get a C or better in the emical engineering majors. There were 64 students from urban or e students succeeded. Another 56 students were from rural or small- lents succeeded in the course. Assume these are random samples. n of urban students succeed in the course as compared to vpothesis. Report the test statistic and p-value. State your Part a: We hope to show that a higher proportion of urban students su the rural students. State the hypotheses. Part b: Perform the significance test on your hypothesis. Report the test statisti. conclusion in terms of the issue. Part c: Give a 95% confidence interval for the difference between th succeed and the proportion of rural students that succeed. interval for the difference between the proportion of urban students that a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem.Explanation / Answer
p1 = 53/61 = 0.87
p2 = 31/56 = 0.55
H0 : p1 = p2
H1: p1 > p2
Pooled sample proportion (P) = (p1 * n1 + p2 * n2)/(n1 + n2)
= (0.87 * 61 + 0.55 * 56)/(61 + 56) = 0.72
SE = sqrt (P * (1 - P) * (1/n1 +;1/n2)
= sqrt (0.72 * 0.28 * (1/61 + 1/56))
= 0.083
The test statistic Z = (p1 - p2)/SE
= (0.87 - 0.55)/0.083 = 3.856
P-value = P(Z > 3.856)
= 1 - P(Z < 3.856)
= 1 - 1 = 0
As p-value is less than the significance level 0.05, so the null hypothesis is rejected.
So there is sufficient evidence to support that the urban students are more successful.
At 95% confidence interval the critical value is 1.96
The confidence interval is
(p1 - p2) +/- z* * SE
= (0.87 - 0.55) +/- 1.96 * 0.083
= 0.32 +/- 0.163
= 0.157, 0.483
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