Question

# A report on Women’s Health claims that at least 35% of women exercise regularly as a...

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 (HA) of p > 35% (i.e. a one-sided test).

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.

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H0 : p = 0.35

Ha : p > 0.35

= x / n = 84 / 200 = 0.42

Test statistic = z

= - P0 / [P0 * (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.

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