An issue that faces individuals investing for retirement is allocating assets among different investment choices.Suppose a study conducted 10 years ago showed that 65% of investors preferred stocks to real estate as an investment.In a recent random sample of 900 investors,540 preferred real estate to stocks.Is this new data sufficient to allow you to conclude that the proportion of investors preferring stocks to real estate has declined from 10 years ago? Conduct your analysis at the α = 0.02 level of significance. A)Because z = -1.915 is not less than -2.055,do not reject H₀.A higher proportion of investors prefer stocks today than 10 years ago. B)Because z = -1.915 is not less than -2.055,do not reject H₀.A lower proportion of investors prefer stocks today than 10 years ago. C)Because z = -3.145 is less than -2.055,reject H₀.A lower proportion of investors prefer stocks today than 10 years ago. D)Because z = -3.145 is less than -2.055,reject H₀.A higher proportion of investors prefer stocks today than 10 years ago.

Question

Quizplus · Accepted Answer

We need to conduct a hypothesis test to see if the proportion of investors who prefer stocks has decreased from 65% to some lower value in the recent years. Let p be the proportion of investors who prefer stocks in the recent years. The null hypothesis H0: p = 0.65 (proportion of investors who prefer stocks is still 65%) and the alternative hypothesis Ha: p < 0.65 (proportion of investors who prefer stocks has decreased).

We use a one-tailed z-test for proportions. The test statistic is z = (p̂ - p) / sqrt(p(1-p)/n), where p̂ is the sample proportion, n is the sample size, and p is the hypothesized population proportion.

In this case, p̂ = 540/900 = 0.6, n = 900, and α = 0.02 (given in the problem). The critical value from the standard normal table for α = 0.02 and a one-tailed test is -2.055.

Calculating the test statistic, we get z = (0.6 - 0.65) / sqrt(0.65(1-0.65)/900) = -3.145.

Since the test statistic is less than the critical value, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the proportion of investors who prefer stocks has decreased from 65% to some lower value in the recent years.

An Issue That Faces Individuals Investing for Retirement Is Allocating