A humane society claims that less than 33% of U.S. households own a dog. In a ra

Question

A humane society claims that less than 33% of U.S. households own a dog. In a random sample of 390 U.S. households, 152 say they own a dog. At =0.01, 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.

Explanation / Answer

a) Ho : p = 0.33

H1 : p < 0.33

critical values is -2.32

p = 152 / 390 = 0.39

Z = 0.39 - 0.33 / ( srqt 0.33*0.67 / 390 )

Z = 2.52

we fail to reject Ho because Z > critical value

conclusuion

there is no evidence to suppor the claim that is less than 33%

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