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?

Let p represents the population proportion.

From the given information, we have

, 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 :

Test statistic :

i.e.

P-value for right tailed test :

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.

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