Question

A sample of 138 men was taken and it was found that 37 owned cats. A sample of 160 women was taken and it was found that 32 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 0.1 significance level.

Claim: Select an answer u 1 < u 2 p 1 ≤ p 2 u 1 > u 2 u 1 ≥ u 2 p 1 ≠ p 2 u 1 ≤ u 2 p 1 < p 2 u 1 = u 2 p 1 ≥ p 2 p 1 > p 2 p 1 = p 2 u 1 ≠ u 2  which corresponds to Select an answer H1: u 1 > u 2 H0: u 1 ≤ u 2 H0: p 1 = p 2 H0: p 1 ≤ p 2 H1: p 1 ≠ p 2 H1: u 1 < u 2 H0: p 1 ≠ p 2 H1: p 1 < p 2 H1: u 1 ≠ u 2 H1: p 1 > p 2

Opposite: Select an answer u 1 ≤ u 2 u 1 ≠ u 2 p 1 = p 2 p 1 < p 2 u 1 ≥ u 2 p 1 ≠ p 2 u 1 = u 2 u 1 > u 2 p 1 ≥ p 2 u 1 < u 2 p 1 > p 2 p 1 ≤ p 2  which corresponds to Select an answer H0: p 1 = p 2 H0: p 1 ≠ p 2 H1: p 1 > p 2 H1: p 1 ≠ p 2 H0: u 1 > u 2 H1: p 1 < p 2 H1: u 1 ≥ u 2 H1: u 1 ≤ u 2 H0: u 1 ≠ u 2 H0: p 1 ≤ p 2 H1: u 1 = u 2

The test is: right-tailed / two-tailed / left-tailed

The test statistic is: z=z=Select an answer 1.39 / 1.22 / 1.11 / 1.05 / 1.87  (to 2 decimals)

The p-value is: Select an answer 0.1469 / 0.1112 / 0.0307 / 0.1335 / 0.1646  (to 4 decimals)

Based on this we: Select an answer / Cannot determine anything / Accept the null hypothesis / Fail to reject the null hypothesis / Reject the null hypothesis

Conclusion There Select an answer ( does / does not ) 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.

Answer 1

The statistical software output for this problem is:

Two sample proportion summary hypothesis test: Pu: proportion of successes for population 1 P2 : proportion of successes for population 2 P1 - P2 : Difference in proportions Ho: P1 - P2 = 0 HA: P1 - P2 = 0 Hypothesis test results: Difference Count1 Totali Count2 Total2 Sample Diff. Std. Err. Z-Stat P-value P1 - P2 3 7 138 32 160 0.068115942 0.049004349 1.3899979 0.1645

Hence,

Claim: p 1 ≠ p 2

H1: p 1 ≠ p 2

Opposite: p1 = p2

H0: p 1 = p 2

Two tailed

Test statistic: 1.39

p - Value: 0.1646

Does not