In the next preview assignment and in the next class, you will be required to describe the sampling distribution of a statistic, use technology to calculate a confidence interval, and interpret the interval in the context of the data.
Is Yawning Contagious?
The objective of this analysis is to explore the proportion of people who yawn after seeing someone else yawn. We will use data from an experiment conducted on the television show Mythbusters. The data are from the yawn dataset in the OpenIntro R package.[1]
In the experiment, 50 participants were randomly assigned to two groups:
- Treatment (34 participants), who saw a person near them yawn
- Control (16 participants), who didn’t see anyone yawn
All of the participants were instructed to wait in a room, and the experimenters recorded whether or not the participants yawned. The participants arrived at different times, so no two participants were in the waiting room at the same time.
We will focus on the data for the 34 participants in the treatment group and analyze the categorical variable yawn with the possible values “yes” and “no.”
Question 1
Make a graphical display of the distribution of yawn using the data in spreadsheet DCMP_STAT_10D_yawn. Use the graph to describe the distribution of the variable.
Question 2
Calculate [latex]\hat{p}[/latex], the proportion of participants in the treatment group who yawned. Round your answer to 3 decimal places.
Question 3
When certain conditions are met, we know the sampling distribution of the sample proportion, [latex]\hat{p}[/latex].
- For large samples, what is the name of the distribution?
- What is the mean of the sampling distribution of the sample proportion? Describe the mean in the context of the data.
- What is the standard error of the sampling distribution of the sample proportion? You can use technology to obtain this value.
Question 4
Now let’s calculate a confidence interval (i.e., a range of plausible values for [latex]p[/latex], the true proportion of people who yawn after seeing someone else yawn).
- Use technology to calculate a 95% confidence interval for [latex]p[/latex].
- Interpret the interval in the context of the data.
Question 5
Suppose you read an article that claims that the true proportion of people who yawn after seeing someone else yawn is 0.63. Based on your analysis, would you be surprised by this claim? Explain.
- Data from the yawn dataset in the OpenIntro R package. https://www.openintro.org/data/index.php?data=yawn ↵
