A humane society clams that less than 36 of US households ow

A humane society clams that less than 36% of U.S. households own a dog. In a random sample of 401 U.S. households, 152 say they own a dog. At a=.03, 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

(e) interpret the decision in the context of the original claim. choose best answer

i. there is eough evidence to support the claim that less than 36% of households own a dog

ii. there is not enough evidence to support the clam that 36% of households own a dog.

iii. There is not enough evidence to support the claim that less than 36% of households own a dog.

iiii. There is enough evidence to support the claim that 36% of households own a dog

Solution

(a) Write the claim mathematically and identify H0 and ha.

Let p be the population proportion

Ho: p=0.36

Ha: p>0.36

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(b) find the critical value(s) and identify the rejection region(s).

It is a right-tailed test.

Given a=0.03, the critical value is Z(0.03)=1.88 (from standard normal table)

So the rejection region is if Z>1.88, we reject Ho.

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(c) find the standardized test statistic.

The test statistic is

Z=(phat-p)/sqrt(p*(1-p)/n)

=(152/401-0.36)/sqrt(0.36*(1-0.36)/401)

=0.79

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(d) Decide whether to reject or fail to reject the null hypothesis

Since Z=0.79 is less than 1.88, we do not reject the null hypothesis.

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(e) interpret the decision in the context of the original claim. choose best answer

iii. There is not enough evidence to support the claim that less than 36% of households own a dog.