Question

A report on Women’s Health claims that at least 35% of women exercise regularly as a way to reduce stress. In order to test this claim, a random sample of 200 women is randomly selected and 84 indicated that they used exercise to reduce stress. Use ?=0.05 and test the above claim.

Hint: Use the null hypothesis (H₀) of p=35% against the alternative hypothesis (H_A) of p > 35% (i.e. a one-sided test).

Which answer below is correct?

Select one:

a. Not enough information to answer.

b. We accept H₀ because 2.075 > 1.645 and conclude that the claim is false.

c. We reject H₀ because 2.075 > 1.645 and conclude that the claim is true.

d. We reject H₀ because 2.075 > 1.282 and conclude that the claim is true.

e. We accept H₀ because 2.075 < 2.326 and conclude that the claim is false.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.35

H_a : p > 0.35

= x / n = 84 / 200 = 0.42

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.42 - 0.35 / [(0.35 * 0.65) / 200]

= 2.075

Critical value = 1.645

Reject the null hypothesis .

c. We reject H₀ because 2.075 > 1.645 and conclude that the claim is true.