Question

In the United States 32% of children live in single-parent households. In a SRS of 350 Hispanic children 37% of them lived in single-parent households. Is this sufficient evidence at alpha=.05 that the proportion of Hispanic children who live in a single-parent household is greater than 32%?

Answer 1

Solution :

This hypothesis test is a one tailed test .

The null and alternative hypothesis is

H₀ : p = 0.32

H_a : p > 0.32

= x / n = 0.37

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.32 - 0.37 / [(0.32 * 0.68) / 350]

= 2.005

P-value = 0.0225

= 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence