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.

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