Question

A researcher claims that 25% of people in the U.S. population have circulation

problems. In a random sample of 189 people, 38 had circulation problems. Test at the

alpha = 0.05 significance level to see if the percent is 25% or if it is less. You should give your

null and alternative hypotheses, then decide if you accept or reject the null hypotheses (find

the test statistic and either the P-value or critical value(s)).

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.25

H_a : p < 0.25

= x / n = 38 / 189 = 0.20106

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.20106 - 0.25 / [(0.25 * 0.75) / 189]

= -1.55

P-value = 0.0601

= 0.05

P-value >

Fail to reject the null hypothesis .