Question

A humane society claims that less than 33​% of U.S. households own a dog. In a random sample of 404 U.S.​ households, 152 say they own a dog. At a =0.10​, is there enough evidence to support the​ society's claim? ​(a) Write the claim mathematically and identify H0 and Ha. ​(b) Find the critical​ value(s) and identify the rejection​ region(s). (c) Find the standardized test statistic.​ (d) Decide whether to reject or fail to reject the null​ hypothesis, and​ (e) interpret the decision in the context of the original claim.

Answer 1

a)

H0: p >= 0.33

Ha: p < 0.33

b)

At 0.10 significance level, critical value is -1.282

Critical region - Reject H0 if test statistics z < -1.282

c)

Sample proportion = 152 / 404 = 0.3762

Test statistics

z = - p / sqrt( p ( 1 - p) / n)

= 0.3762 - 0.33 / sqrt( 0.33 * 0.67 / 404)

= 1.975

d)

Since test statistics falls in non-rejection region, we do not have sufficient evidence to reject H0.

e)

We conclude at 0.10 level that we fail to support the claim that less than 33​% of U.S. households own a dog.