Television shows often add laugh tracks to make the show seem funnier. Does doing the same thing with “dad jokes” make them funnier? The researchers (Cai et al., 2019) had a professional comedian record 40 dad jokes. (e.g. What is brown and sticky? A stick. What did the duck do when he read all these jokes? He quacked up.) They had people listen to these jokes and rate how funny they thought they were on a 7-point scale. The mean rating for each of these 40 jokes was calculated. Other people listened to the same 40 jokes, but this time they included a laugh track made up of posed laughter. (They just asked people to laugh and recorded the results and then added it in after each joke.) The mean rating for each joke with the laughter was calculated. From these data the increase in the rating with the laugh track for each joke was calculated. Positive numbers indicate an increase in the rating with a laugh track and negative numbers indicate a decreased rating with the laugh track. These results are in the file LaughIncrease. We want to determine whether laughter tends to increase the rating of how funny people think the joke is (which is the same as having a mean increase in rating greater than 0).

a. Write out the null and alternative hypotheses for our test in words or in symbols. 

b. Open the One Mean applet, choose the Bootstrapping option at the top, and paste in the data. What are the mean and standard deviation for the data? 

c. Use the applet to take at least 10,000 samples of an appropriate size from the data to develop a bootstrap distribution of sample means. What is the standard deviation of the bootstrap sampling distribution? 

d. Shift the sample data so its mean is as close to 0 as possible. Using the shifted bootstrap sampling distribution, what is your p-value and what conclusion can you make?