Module 17: Background You’ll Need 4

  • Know how confidence intervals for a difference in means are interpreted

Interpreting Confidence Intervals for a Difference in Means

Recall that a confidence interval for a difference in population means is interpreted as an interval of plausible values for the difference in means.

Suppose that each student in a random sample of [latex]50[/latex] first-year students at a college and each student in a random sample of [latex]50[/latex] second-year students from the college are asked how many hours of sleep they get on a typical weekday night. The data from these two samples are used to construct a confidence interval for the difference [latex]\mu_F - \mu_S[/latex], where [latex]\mu_F[/latex] is the mean number of sleep hours for first-year students and [latex]\mu_S[/latex] is the mean number of sleep hours for second-year students. Because the samples are random samples and the sample sizes are both greater than [latex]30[/latex], it would be appropriate to use a two-sample [latex]t[/latex] confidence interval.

If the [latex]95\%[/latex] confidence interval was [latex](0.4, 1.0)[/latex], we would note the following:

  • Plausible values for are between [latex]0.4[/latex] and [latex]1.0[/latex].
  • All of the plausible values are positive, which corresponds to [latex]\mu_F[/latex] being greater than [latex]\mu_S[/latex].
  • We are [latex]95\%[/latex] confident that the mean number of hours of sleep for first-year students is greater than the mean number of hours of sleep for second-year students by somewhere between [latex]0.4[/latex] and [latex]1.0[/latex] hours.