Question

Test the claim that the proportion of people who own cats is larger than 10% at the 0.10 significance level. The null and alternative hypothesis would be: H 0 : p ≤ 0.1 H a : p > 0.1 H 0 : μ ≤ 0.1 H a : μ > 0.1 H 0 : μ = 0.1 H a : μ ≠ 0.1 H 0 : p = 0.1 H a : p ≠ 0.1 H 0 : p ≥ 0.1 H a : p < 0.1 H 0 : μ ≥ 0.1 H a : μ < 0.1 The test is: two-tailed left-tailed right-tailed Based on a sample of 300 people, 17% owned cats The p-value is: (to 2 decimals) Based on this we: Reject the null hypothesis Fail to reject the null hypothe

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.10

H_a : p > 0.10

= 0.17

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.17 - 0.10 / [(0.10 * 0.90) / 300]

= 4.04

P-value = 0.000

= 0.10

P-value <

Reject the null hypothesis .

There is sufficient evidence to suggest that   the proportion of people who own cats is larger than 10% at the 0.10 significance level.