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=84,n2=89,x1=57x2=64First-Years (Pop. 1):n1=84,x1=57Fourth-Years (Pop. 2):n2=89,x2=64
Is there evidence, at an α=0.1, 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 standardized test statistic=
Note: For the next part, your answer should use interval notation. An answer of the form (−∞,a)(−∞,a) is expressed (-infty, a), an answer of the form (b,∞)(b,∞) is expressed (b, infty), and an answer of the form (−∞,a)∪(b,∞)(−∞,a)∪(b,∞) is expressed (-infty, a)U(b, infty).
B. The rejection region for the standardized test statistic:
C. The p-value is
(A)
H0: Null Hypothesis: p1 = p2 ( There is no difference in proportions between first-years and fourth-years)
HA: Alternative Hypothesis: p1
p2 ( There is a difference in proportions between first-years and
fourth-years) (Claim)
n1 = 84
1
= 57/84 = 0.6786
n2 = 89
2
= 64/89 = 0.7191
Pooled Proportion is given by:
Test Statistic is given by:
So,
The value of the standardized test statistic= - 0.581
(B)
= 0.10
From Table, critical values of Z =
1.64
The rejection region for the standardized test statistic:
(-infty, - 1.64)U(1.64, infty).
(C)
By Technology:
The p-value is 0.5612
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