Question

According to a study by the American Pet Food​ Dealers' Association,​ 63% of U.S. households own pets. A report was prepared for an editorial in the newspaper of a large city. In the​ report, a test of hypothesis was performed in order to see whether there was evidence that the actual proportion of U.S. households that own pets is significantly different from​ 63%. Assuming that a random sample of 300 U.S. households was obtained with 172 of them having pets and using a​ 2% level of​ significance, which of the following is​ correct?

A.

​p-value (to 3 decimal​ places) is​ 0.019; reject the null hypothesis

B.

​p-value (to 3 decimal​ places) is​ 0.042; fail to reject the null hypothesis

C.

​p-value (to 3 decimal​ places) is​ 0.019; fail to reject the null hypothesis

D.

​p-value (to 3 decimal​ places) is​ 0.042; reject the null hypothesis

E.

None of the above

Answer 1

Here we have n=300 X=172 Ô X _172 -- n =0.5733 300 Hypothesis Ho: P=0.63 Ha: P 0.63 This is a two tailed test. Test statistics 0.5733-0.63 Z = P-P P(1-P)/n 0.63(1-0.63) 300 -2.03 WWW Pvalue Pvalue at Z= |-2.03|

Pvalue = P(2>2.03)* 2 = 2*(1-P(Z<2.03) = 2*(1-0.9788215) = 0.042357 = 0.042 (Round to 3 decimal places) Correct option B. P-value is 0.042; fail to reject the null hypothesis.