Question

An annual survey of first-year college students asks 274,000 students about their attitudes on a variety of subjects. According to a recent survey, 58% of first-year students believe that abortion should be legal. Use a 0.05 significance level to test the claim that over half of all first-year students believe that abortion should be legal.

H0: p=0.5 Ha: p>0.5

Find the test statistic z=?

Find p?

reject or don't reject due to not enough evidence or there is enough evidence?

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.5

H_a : p > 0.5

= 0.58

P₀ = 0.5

1 - P₀ = 0.5

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.58 - 0.5 / [(0.5 * 0.5) / 274000]

= 83.8

P(z > 83.8) = 1 - P(z < 83.8) = 1 - 1 = 0

P-value = 0

= 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence to test the claim that over half of all first-year students believe that abortion should be legal .