Question

In a survey of 700 US adults with children, 270 of them reported that they saved money for their children’s college education. Can you conclude that more than one third (33%) of US adults with children have saved money for college? Use a 0.05 significance level.

a. State the null (H0) and alternative (H1) hypotheses.

b. Give the test statistics and the p-value for this significance test.

c. Make a decision on whether or not to reject the null hypothesis.

d. Summarize the conclusion in the context of this problem.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ : p = 0.33

H_a : p $\neq$ 0.33

n = 700

x = 270

$\hat p$ = x / n = 270 / 700 = 0.3857

P₀ = 0.33

1 - P₀ = 1 - 0.33 = 0.67

z = $\hat p$ - P₀ / [$\sqrt$P_{0 *} (1 - P₀ ) / n]

= 0.3857 - 0.33 / [$\sqrt$(0.33 * 0.67) / 700]

= 3.135

This is the right tailed test .

P(z > 3.135) = 1 - P(z < 3.135) = 1 - 0.9991 = 0.0009

P-value = 0.0009

$\alpha$ = 0.05

P-value < $\alpha$

Reject the null hypothesis .

one third (33%) of US adults with children have saved money for college .