Question

According to a  Lawyers.com survey, only 35% of adult Americans had a will (The Wall Street Journal, December 12). Suppose a recent survey of 250 adult Americans found 100 adults with wills.

a. Specify the competing hypotheses to determine whether the proportion of adult Americans who have a will differs from the proportion reported .

b. Calculate the value of the test statistic and the p-value.

c. At the 5% significance level, is the proportion different? Explain.

Answer 1

Solution....

a) H0: Pu=0.35 (sample proportion is equal to population proportion)

H1:Pu not equal to 0.35 (Sample proportion is different from population proportion)

b) For largesample, compute 1-proportion Z test.

Z=(Ps-Pu)/sqrt [Pu(1-Pu)/N], where, Ps and Pu refer to sample proportion and population proportion, N is the sample size.

=(100/250-0.35)/sqrt [0.5(1-0.5)/250]

=1.58

The p value is 0.114107.

c) The p value is not less than alpha=0.05. Therefore, fail to reject null hypothesis. There is not sufficient sample evidence to conclude that proportion of adult Americans that have a will differs from the proportion reported in 2009.