Question

Test the claim that the proportion of women who own sports cars is smaller than the proportion of men who own sports cars at the .025 significance level.

Based on a sample of 80 women, 40% owned sports cars
Based on a sample of 60 men, 55% owned sports cars

The test statistic is:  (to 3 decimals)

The p-value is:  (to 3 decimals)

Based on this we:

• Fail to reject the null hypothesis
• Reject the null hypothesis

Answer 1

The statistical software output for this problem is:

Two sample proportion summary hypothesis test: P1 : 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 32 80 33 60 -0.15 0.085173143 -1.7611185 0.0391

Hence,

Test statistic = -1.761

p - Value = 0.039

Fail to reject the null hypothesis