Question 1071804: A marketing research company contacted 600 married women and 400 men. All owned big plasma TVs. Two hundred of the women and 150 of the men replied they spent more time watching their plasma TV than with their spouses. A- At the 0.05 significance level , is there a difference between the response of women and men? ( use the five step method) B- determine the p-value and interpret the results
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! Our sampling statistic is the proportion, namely
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N1 = 600 and N2 = 400
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women(p1) is 200/600 = 1/3 and men(P2) is 150/400 = 3/8
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A) At 0.05 significance level
Ho: P1 = P2 and Ha: P1 not = P2
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P = (200 + 150) / (600 + 400) = 350 / 1000 = 0.35
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standard error(SE) = square root(0.35 * 0.65) = 0.477
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test statistic(z-value) = ((1/3) - (3/8)) / SE = -0.0874
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since our Ho has an =, we use a two tailed test
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Therefore we split the 0.05 between the the high and low probabilities, that is 0.05/2 = 0.025
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The associated z-scores for 0.025 is -1.96 and 1.96
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Our test statistic(-0.0874) is not less than -1.96 and
0.0874 is not greater than 1.96
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Therefore we can not reject our Ho
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B) Since we have a two-tailed test, the P-value is the probability that the z-score is less than -0.0874 or greater than 0.0874.
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Use z-tables or a Normal Distribution Calculator to find P(z < -0.0874) = 0.4641, and P(z > 0.0874) = 0.4641. Thus, the P-value = 0.4641 + 0.4641 = 0.9282.
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Since the P-value (0.9282) is greater than the significance level (0.05), we accept the null hypothesis.
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