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In: Statistics and Probability

In terms of acting, Betty White is known for starring on 3 different long running television...

  1. In terms of acting, Betty White is known for starring on 3 different long running television shows (The Mary Tyler Moore Show, The Golden Girls and Hot In Cleveland). Those three shows averaged 23.7 shows per season. However, it seems that shows are producing few episodes per season, and Betty decides to put that to the test. She takes a random sample of long running television programs and determined the number of episodes in their most recent season below:

13, 26, 23, 18, 24, 18, 19, 13, 13, 15, 16, 21, 20, 16, 26

You may assume that the data comes from a normal distribution.

  1. Construct a 95% confidence interval for the average number of episodes per season for a television program

  1. Based on your answer to (a), can we say that the average number of episodes per season is lower than the value 23.7, the average number of episodes for the shows that Betty starred in? Explain.

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