A market researcher is interested in determining whether the age of listeners influences their preferred musical styles. The following is a contingency table from a random sample of 385 individuals: The researcher uses $\alpha$= 0.05. The appropriate decision is ___.
A) reject the null hypothesis and conclude the two variables are not independent
B) reject the null hypothesis and conclude the two variables are independent
C) do not reject the null hypothesis and conclude the two variables are not independent
D) do not reject the null hypothesis and conclude the two variables are independent
E) do nothing

Question

A market researcher is interested in determining whether the age of listeners influences their preferred musical styles. The following is a contingency table from a random sample of 385 individuals:  The researcher uses $\alpha$= 0.05. The appropriate decision is ___.
A) reject the null hypothesis and conclude the two variables are not independent 
B) reject the null hypothesis and conclude the two variables are independent 
C) do not reject the null hypothesis and conclude the two variables are not independent 
D) do not reject the null hypothesis and conclude the two variables are independent 
E) do nothing

Quizplus · Accepted Answer

To determine whether age and preferred musical styles are independent variables, we need to conduct a chi-square test. Given the contingency table and significance level of 0.05, we can use a chi-square test to determine whether the observed frequencies are significantly different from the expected frequencies. After conducting the test, if the calculated chi-square value is greater than the critical value, we reject the null hypothesis and conclude that the two variables are not independent. In this case, the calculated chi-square value is greater than the critical value, so we reject the null hypothesis and conclude that age and preferred musical styles are not independent. Therefore, the appropriate decision is to choose A.

A Market Researcher Is Interested in Determining Whether the Age α\alphaα

A Market Researcher Is Interested in Determining Whether the Age $\alpha$