Question 799492: In a sample of 50 men, 44 said that they had less leisure time today than they had 10 years
ago. In a sample of 50 women, 48 women said that they had less leisure time than they
had 10 years ago. What is the test statistic? At á = .05, is there a
difference in the proportions between the men and women?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In a sample of 50 men, 44 said that they had less leisure time today than they had 10 years ago.
In a sample of 50 women, 48 women said that they had less leisure time than they
had 10 years ago.
What is the test statistic?
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p-hat men:: 44/50 = 0.22
p-hat women:: 48/50 = 0.24
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Test Stat:
z(0.24-0.22) = (0.02)/sqrt[(0.22*0.78/50)+(0.24*0.76/50)] = 0.2377
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At á = .05, is there a difference in the proportions between the men and women?
p-value = 2*P(z > 0.2377) = 0.8121
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Since the p-value is greater than 5%, fail to reject Ho.
Ho: p(men)-p(women) = 0
Ha: p(men)-p(women) # 0
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Cheers,
Stan H.
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