Question

A recent study claimed that at least 15% of junior high students are overweight. In a sample of 160 students, 18 were found to be overweight. At α = 0.05, test the claim. Identify the claim, state the null and alternative hypotheses, find the critical value, find the standardized test statistic, make a decision on the null hypothesis (you may use a P-Value instead of the standardized test statistic), write an interpretation statement on the decision.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.15

H_a : p 0.15

n = 160

x = 18

= x / n = 18 / 160 = 0.11

P₀ = 0.15

1 - P₀ = 1 - 0.15 = 0.85

The information provided, the significance level is α =0.05, and the critical value for a two-tailed test is z_{c ​}=1.96

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.11- 0.15 / [0.15 * 0.85) /160 ]

= −1.328

Test statistic = z = −1.33

P-value = 0.1840

= 0.05

P-value  ≥

0.1840 ≥ 0.05

Fail to reject the null hypothesis .Therefore, there is not enough evidence to claim that the population proportion p is different than P₀