Activity: How Much Do Students Sleep?

Objective

You will create your own confidence interval for estimating on average how much college students sleep.

Instructions

  1. Form a group of three or four. (This is your sample size!)

  2. Record how many hours of sleep each one of you got last night. No need to be integers. Sleeping 7.6 hours totally works! So please use decimal hours as your data. Don’t know decimal hours for 7 hours 20 minutes? Use the app below for the answer!

  1. Construct your 95% confidence interval for mean sleeping hours using the formula

\[ \left[ \bar{x} - t_{0.025, n-1} \frac{s}{\sqrt{n}}, \, \bar{x} + t_{0.025, n-1} \frac{s}{\sqrt{n}} \right]\]

where \(\bar{x}\) is the sample mean, \(s\) is the sample standard deviation, \(n\) is the sample size, and \(t_{0.025, n-1}\) is the \(t\) critical value such that \(P(T > t_{0.025, n-1}) = 2.5\%\).

  1. Let’s create a larger sample by considering all of your sleeping hours. Construct its 95% confidence interval. Note that you need to obtain new \(\bar{x}\), \(s\), \(n\), and \(t_{0.025, n-1}\).

Discussion

  1. What does this interval mean in words?

  2. Does the CI tell us about individual sleep hours or about the average student’s sleep?

  3. If we repeated this process with new samples, would every interval capture the true population mean?

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