SOLUTION: Two random samples are taken, one from among first-year students and the other from among fourth-year students at a public university. Both samples are asked if they favor modifyin

Question 1206985: Two random samples are taken, one from among first-year students and the other from among fourth-year students at a public university. Both samples are asked if they favor modifying the student Honor Code. A summary of the sample sizes and number of each group answering
yes'' are given below:
First-Years (Pop. 1):Fourth-Years (Pop. 2):n1=97,n2=91,x1=56x2=60
Is there evidence, at an α=0.055
level of significance, to conclude that there is a difference in proportions between first-years and fourth-years? Carry out an appropriate hypothesis test, filling in the information requested.
A. The value of the test statistic (rounded to 3 decimal places):
Note: For the next part, your answer should use interval notation. An answer of the form (−∞,a)
is expressed (-infty, a), an answer of the form (b,∞)
is expressed (b, infty), and an answer of the form (−∞,a)∪(b,∞)
is expressed (-infty, a)U(b, infty).
B. The rejection region for the standardized test statistic:
C. The p-value is
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
using pooled standard error, i get z = -1.156.

using un-pooled standard error, i get z = -1.161.

the two-tailed alpha is equal to .055.
that would be a tail of alpha/2 = .0275 on the left and a tail of alpha/2 = .0275 on the right.

at .055 two tailed alpha, the critical z-score is plus or minus 1.9189.

z-score of -1.156 and -1.161 are less than -1.9189, so the results are not significant regardless if you used pooled or un-pooled standard error.

answers to your questions:

A. test statistic is z = -1.156 (pooled standard error is assumed).

B. the rejection region for the test is z = (-infinity,-1.9189) union (1.9189,infinity).
C. the p-value of the test is .2476.
that's a two-tailed p-value, meaning half is on the left tail and half is on the right tail.

here's what the results look like on a z-score calculator.

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