A sample of 136 men was taken and it was found that 54 owned cats. A sample of 1
ID: 3362391 • Letter: A
Question
A sample of 136 men was taken and it was found that 54 owned cats. A sample of 113 women was taken and it was found that 34 owned cats. Test the claim that the proportion of men who own cats is different from than the proportion of women who own cats at the 0.05 significance level. Claim: which corresponds to Opposite: which corresponds to The test is: The test statistic is: z = z = (to 2 decimals) The p-value is: (to 4 decimals) Based on this we: Conclusion There appear to be enough evidence to support the claim that the proportion of men who own cats is different from than the proportion of women who own cats.
Explanation / Answer
Null Hypothesis H0: The proportion of men who own cats is same as the proportion of women who own cats.
Alternative Hypothesis Ha: The proportion of men who own cats is different from than the proportion of women who own cats.
Pooled sample proportion = (p1 * n1 + p2 * n2) / (n1 + n2)
where p1 , p2 are the sample proportions of men and women and n1 and n2 are the sample size of men and women.
p1 = 54/ 136 = 0.397
p2 = 34 / 113 = 0.3
Pooled sample proportion = (0.397 * 136 + 0.3 * 113) / (136 + 113 ) = 0.353
The standard error (SE) of the sampling distribution difference between two proportions.
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = sqrt{ 0.353 * ( 1 - 0.353 ) * [ (1/136) + (1/113) ] } = 0.061
Test statistic, z = (Difference in proportions) / SE = (0.397 - 0.3) / 0.061 = 1.59
p-value = P(z > 1.59) = 0.0559
As, p-value is less than the 0.05 significance level, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that the proportion of men who own cats is different from than the proportion of women who own cats.