Question

For each question please state your null and alternative hypothesis, your p-value and conclusion of your hypothesis test. You may use your calculator to perform the hypothesis.

A roper Poll claims that 5% of U.S. adults have had vivid dreams about UFOs. You decide to test this claim and ask a random sample of 250 U.S. adults whether they have had vivid dreams about UFOs. Of those surveyed, 8% reply yes. A the .01 significance level , is there enough evidence to reject the claim?

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.05

H_a : p 0.05

n = 250

= 0.08

P₀ = 0.05

1 - P₀ = 1 - 0.05 = 0.95

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.08 - 0.05 / [(0.05 * 0.95) / 250]

= 2.18

Test statistic = 2.18

P(z > 2.18) = 1 - P(z < 2.18) = 1 - 0.9854 = 0.0146

P-value = 2 * 0.0146 = 0.0292

= 0.01

P-value >

Fail to reject the null hypothesis .

There is no enough evidence to reject the claim .