Question

A researcher claims that the proportion of college students who plan to participate in community service after graduation is greater than 35%. To test this claim, a survey asked 500 randomly selected college students if they planned to perform community service after graduation. Of those students, 195 indicated they planned to perform community service. The following is the setup m the following hypothesis test: H0:p=0.35 Ha:p>0.35 In this example, the p-value was determined to be 0.030. Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%) .

Select the correct answer below: The decision is to reject the Null Hypothesis. The conclusion is that there is enough evidence to support the claim. The decision is to fail to reject the Null Hypothesis. The conclusion is that there is not enough evidence to support the claim.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p =0.35

H_a : p > 0.35

n =500

x = 195

= x / n = 195 / 500 = 0.39

P₀ = 0.35

1 - P₀ = 1 - 0.35 = 0.65

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.39 -0.35/ [0.35 * 0.65 /500 ]

= 1.875

Test statistic = z = 1.87

P(z >1.87 ) = 1 - P(z < 1.87 ) = 1 - 0.9693

P-value = 0.0307

= 0.05

P-value <

0.0307 < 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that