Question 1063368: Two boxes, A and B contain equal numbers of balls (black and white). A sample of
100 balls selected with replacement from each of the boxes revealed 52 white balls form box A and 44
white balls from box B.
1. Test the hypothesis that the two boxes have equal ratio of white balls, using a significance level of 0.05
2. Test the hypothesis that box A has greater ratio of white balls than box B, using a significance level of
0.05
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Ho: p1=p2; p1=A and p2=B
Ha=p1 NE p2
alpha=0.05 P reject Ho|Ho true
test statistic is z
Critical value |z|>1.96
z=(p1-p2) divided by SE, where SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }; pooled proportion is 0.48
z=0.08/sqrt (0.48*0.52*(1/50))=0.08/0.07065=1.13
fail to reject Ho, and there is insufficient evidence there is a significant difference between the two boxes in regard to number of white balls.
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With a one-tail test,
Ho: p1 <= p2
Ha: p1 > p2
Everything is the same except now the critical value is z> 1.645. All the rejection region is on one side of the curve.
Still fail to reject, however, although the p-value is smaller, going from 0.26 to 0.13, halving it.
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