MATH SOLVE

3 months ago

Q:
# In 2003, 6 percent of vacation-home owners were minorities. The National Association of Realtors (NAR) reported the results of a May 2006 survey of vacation-home owners. In a sample of 416 households that owned one or more vacation homes, 46 were minorities. Do the survey results allow the NAR to conclude at a 0.01 level of significance that the percentage of vacation-home owners who are minorities is larger than 6 percent?

Accepted Solution

A:

Answer with explanation:Let p represents the population proportion.From the given information, we have[tex]H_0: p=0.06\\\\H_a: p>0.06[/tex], since alternative hypothesis is right tailed then the test is right tailed test.Given : In a sample of 416 households that owned one or more vacation homes, 46 were minorities. i.e. n= 416 Sample proportion : [tex]\hat{p}=\dfrac{46}{416}=0.110576923077\approx0.11[/tex]Test statistic : [tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]i.e. [tex]z=\dfrac{0.11-0.06}{\sqrt{\dfrac{0.06(1-0.06)}{416}}}[/tex][tex]\Rightarrow\ z=4.29414907893\approx4.29[/tex]P-value for right tailed test : [tex]P(z>4.29)=1-P(z\leq4.29)[/tex][tex]=1-0.999991=0.0000089[/tex]Since the p-value is less than the significance level (0.01), so we reject the null hypothesis.Thus , we conclude that we have enough evidence to support the claim that that the percentage of vacation-home owners who are minorities is larger than 6 percent.