Question

A Gallop Poll reports that 60% of adults fear public speaking. A student believes that the proportion among her classmates is SIGNIFICANTLY higher. She does a survey of 40 classmates and finds that 30 of them fear public speaking. Perform a hypothesis test at the 5% significance level.

State the Null Hypothesis, Alternative Hypothesis, and the p-value for the hypothesis test.

Then state your Decision (Reject H0 or Do Not Reject H0) and your Conclusion.

Answer 1

Solution :

This hypothesis test is a right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.60

H_a : p > 0.60

= x / n = 40 / 30 = 0.75

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.75 - 0.60 / [(0.60 * 0.40) / 40]

= 1.936

P-value = 0.0264

= 0.05

P-value <

Reject the null hypothesis (H0)