Imagine that before the debate, a sample of 75 likely voters had 41 who preferred candidate A. After the debate, a separate sample of 75 likely voters had 34 who preferred candidate A. Determine if the support for candidate A decreased after the debate, using alpha=0.10. By hand.
Imagine that before the debate, a sample of 75 likely voters had 41 who preferred candidate A. After the debate, a separate sample of 75 likely voters had 34 who preferred candidate A. Determine if the support for candidate A decreased after the debate, using alpha=0.10. By hand.
Solution:
Let X1 be the number of voters who preferred candidate A before the debate, X2 bet the number of voters who preferred candidate A after the debate, n1 be the sample number of likely voters before the debate and n2 be the sample number of likely voters after the debate.
From the given information, Xl=41, n1=75, X2=34 and n2=75.
State the hypotheses.
Null hypothesis:
H0: pl–p2≤0
That is, the support for candidate A is not decreased after the debate.
Alternative hypothesis:
H1: pl–p2>0
That is, the support for candidate A is decreased after the debate.
The sample proportions are
The pooled proportion is
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