Question

Researchers at the University of Pennsylvania studied the humor of late-night comedians Jon Stewart, Jay Leno, and David Letterman. Between July 15 and September 16, 2004, they performed a content analysis of the jokes made by Jon Stewart during the “headlines” segment of The Daily Show and by Jay Leno and David Letterman during the monologue segments of their shows. (We will consider this a random sample of all their jokes.) A summary of the data that they gathered was:  

• Leno: 315 of the 1313 jokes were of a political nature

• Letterman: 136 of the 648 jokes were of a political nature

• Stewart: 83 of the 252 jokes were of a political nature

When this test is run a p-value = 0.0008 is found. Follow-up confidence intervals for all the pairwise differences in proportions are shown below. Explain what information these confidence intervals give you as to which comedian tells a higher proportion of political jokes than the others in the long run and which ones aren’t significantly different (if any).  

• -0.009 to 0.069: Leno – Letterman

• -0.152 to -0.027: Leno – Stewart

• -0.185 to -0.054: Letterman – Stewart

Answer 1

• -0.009 to 0.069: Leno – Letterman

The Confidence interval for the difference of political jokes nature includes the value zero. Hence, there is no significant difference in political jokes nature between Leno and Letterman.

• -0.152 to -0.027: Leno – Stewart

The Confidence interval for the difference of political jokes nature does not include the value zero. Hence, there is a significant difference in political jokes nature between Leno – Stewart. Also, the political jokes nature of Leno is less than Stewart.

• -0.185 to -0.054: Letterman – Stewart

The Confidence interval for the difference of political jokes nature does not include the value zero. Hence, there is a significant difference in political jokes nature between Letterman and Stewart. Also, the political jokes nature of Letterman is less than Stewart.

So, Stewart has the highest  political jokes nature among them.