(1 point) Two random samples are taken, one from among first-year UVA students a
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(1 point) Two random samples are taken, one from among first-year UVA students and the other from among fourth-year UVA students. Both samples are asked if they favor modifying the Honor Code. A summary of the sample sizes and number ofeach group answering yes" are given below: First-Years (Pop. 1) n1 86. z1 48 Fourth-Years (Pop. 2): n2 97, r2 63 s there evidence, at an a 0.065 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 B. The p-value is C. Your decision for the hypothesis test: A. Reject H1 B. Reject Ho C. Do Not Reject Ho o D. Do Not Reject HExplanation / Answer
n1 = 86 , n2 = 97 x1 = 48 x2 = 63
so p1 = 48/86 = 0.56 , p2 = 63/97 = 0.65
pooled sample proportion is
p = (p1 * n1 + p2 * n2) / (n1 + n2)
(0.56*86 + 0.65*97)/(86+97) = 0.607
Standard error. Compute the standard error (SE) of the sampling distribution difference between two proportions.
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
=sqrt(0.607*(1-0.607)*(1/86 + 1/97)) = 0.0723
Now the z stat is
z = (p1 - p2) / SE
= (0.56-0.65)/0.0723 = -1.244
from the z tables the p value is
0.10675
hence as the p value is not less than 0.065, hence we fail to reject the null hypothesis
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