Question

An organization surveyed 1000 teens and 1000 parents of teens to learn about how teens are using social networking sites such as Facebook and MySpace. The two samples were independently selected and were chosen in a way that makes it reasonable to regard them as representative of American teens and parents of American teens.

(a)

When asked if they check their online social networking sites more than 10 times a day, 221 of the teens surveyed said yes. When parents of teens were asked if their teen checked his or her site more than 10 times a day, 40 said yes. Use a significance level of 0.01 to carry out a hypothesis test to determine if there is convincing evidence that the proportion of all parents who think their teen checks a social networking site more than 10 times a day is less than the proportion of all teens who report that they check more than 10 times a day. (Use p_teens − p_parents. Round your test statistic to two decimal places and your P-value to four decimal places.)

z=

P-value=

State your conclusion.

We reject H₀. We do not have convincing evidence that the proportion of teens who report that they check a social networking site more than 10 times a day is greater than the proportion of parents of teens who think their teens check more than 10 times a day.We fail to reject H₀. We do not have convincing evidence that the proportion of teens who report that they check a social networking site more than 10 times a day is greater than the proportion of parents of teens who think their teens check more than 10 times a day.    We reject H₀. We have convincing evidence that the proportion of teens who report that they check a social networking site more than 10 times a day is greater than the proportion of parents of teens who think their teens check more than 10 times a day.We fail to reject H₀. We have convincing evidence that the proportion of teens who report that they check a social networking site more than 10 times a day is greater than the proportion of parents of teens who think their teens check more than 10 times a day.

(b)

The article also reported that 375 of the teens surveyed said they had posted something on their networking site that they later regretted. Would you use the two-sample z test of this section to test the hypothesis that more than one-third of all teens have posted something on a social networking site that they later regretted? Explain why or why not.

No. Here we're comparing two sample proportions, so a one-sample test for a proportion should be used.Yes. Here we're comparing two sample proportions, so a two-sample test for a proportion should be used.    No. Here we're comparing a single sample proportion to a hypothesized population proportion, so a one-sample test for a proportion should be used.Yes. Here we're comparing a single sample proportion to a hypothesized population proportion, so a two-sample test for a proportion should be used.

(c)

Using an appropriate test procedure, carry out a test of the hypothesis given in part (b). Use

α = 0.05

for this test. (Round your test statistic to two decimal places and your P-value to four decimal places.)

z=

P-value=

State the conclusion in the problem context.

Reject H₀. We have convincing evidence that more than one-third of all teens have posted something on a social networking site that they later regretted.

Do not reject H₀. We do not have convincing evidence that more than one-third of all teens have posted something on a social networking site that they later regretted.    

Reject H₀. We do not have convincing evidence that more than one-third of all teens have posted something on a social networking site that they later regretted.

Do not reject H₀. We have convincing evidence that more than one-third of all teens have posted something on a social networking site that they later regretted.

Answer 1