Question

The report "How Teens Use Media" (Nielsen, June 2009) says that \(83 \%\) of U.S. teens use text messaging. Suppose you plan to select a random sample of 400 students at the local high school and ask each one if he or she uses text messaging. You plan to use the resulting data to decide if there is evidence that the proportion of students at the high school who use text messaging differs from the national figure given in the Nielsen report. What hypotheses should you test?

Short answer

The Null Hypothesis is \(H_0: P = 0.83\) and the Alternative Hypothesis is \(H_a: P \neq 0.83\).

Step-by-step solution

Formulate the Null Hypothesis (\(H_0\))

Start by stating the null hypothesis. This hypothesis posits that there is no significant difference between the observed and expected value. Here, it's presumed that the proportion of the local high school's students that use text messaging \(P\), is equal to the national proportion of students that use text messaging at 83% or \(0.83\). So, \(H_0: P = 0.83\).

Formulate the Alternative Hypothesis (\(H_a\))

The alternative hypothesis asserts that there is a significant difference between the observed and expected value. For this problem, the alternative hypothesis would be that the proportion of the local high school's students who use text messaging \(P\), is not equal to the national proportion of 83% or \(0.83\). So, \(H_a: P \neq 0.83\).