A humane society claims that less than 37 % of U.S. households own a dog. In a r

Question

A humane society claims that less than 37 % of U.S. households own a dog. In a random sample of 409 U.S. households, 152 say they own a dog. At a=0.04, 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.

(a) Which of the following correctly states H0 and Ha?

(b) What is (are) the critical value(s)?

(c) What is the standardized test statistic?

(d) Which of the following is the correct conclusion for the test?

Explanation / Answer

a. Here claim is that less than 0.37 household owns a dog

Hence hypothesis are

H0: p>=0.47 Vs H1:p<0.37

b. z critical value is -1.7507

c. phat=152/409=0.372

SEp=sqrt(pq/n)=sqrt((0..37*0.63)/409)=0.024

Hence test statistic is z=(phat-p)/SEp=(0.372-0.37)/0.024=0.0833

d. P value of the test is P(z<0.083)=0.5332>alpha=0.05 hence we do not reject the null hypothesis

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