SOLUTION: Test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the .025 significance level. The null and alternative hypothesis woul

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Question 1170285: Test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the .025 significance level. The null and alternative hypothesis would be:
The test is:
left-tailed
two-tailed
right-tailed
Based on a sample of 80 men, 25% owned cats
Based on a sample of 40 women, 30% owned cats The test statistic is:
(to 2 decimals) The critical value is:
(to 2 decimals) Based on this we:
Reject the null hypothesis
Fail to reject the null hypothesis
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Ho: p men >= p women
Ha: p men < p women
left tailed, because we suspect p men < p women
men is 20/80 or 0.25
women is 12/40 or 0.3
the critical value is z<-1.96
the numerator is the difference between 0.25 and 0.3 or -0.05
the denominator is sqrt ((.25.*.75/80)+(.3.*.7/40))=sqrt(0.0075)=0.0868
z is -0.58.Fail to reject; insufficient evidence to show a difference.