Question

The National Longitudinal Study of Adolescent Health interviewed a random sample of $4877$teens (grades $7$to $12$). One question asked, “What do you think are the chances you will be married in the next $10$years?” Here is a two-way table of the responses by gender:

Which of the following is the appropriate null hypothesis for performing a chi-square test?

a. Equal proportions of female and male teenagers are almost certain they will be married in $10$years.

b. There is no difference between the distributions of female and male teenagers’ opinions about marriage in this sample.

c. There is no difference between the distributions of female and male teenagers’ opinions about marriage in the population.

d. There is no association between gender and opinion about marriage in the sample.

e. There is no association between gender and opinion about marriage in the population.

Short answer

Option (e)$H_o$: There is no correlation between gender and population opinion on marriage.

$H_a$: In the population, there is a link between gender and attitudes toward marriage.

Step-by-step solution

Given information

We have to determine the state the null and alternative hypotheses.

Simplification

The null and alternative hypotheses:

  $H_0$: There is no correlation between gender and population opinion on marriage.

  $H_a$: In the population, there is a link between gender and attitudes toward marriage.

Hence, option e is correct.