Flat Tire and Missed Class. A classic story involves four carpooling students who missed a test and gave as an excuse a flat tire. On the makeup test, the instructor asked the students to identify the particular tire that went flat. If they really didn't have a flat tire, would they be able to identify the same tire that went flat? The author asked 41 other students to identify the tire they would select. The results are listed in the following table. Use a 0.05 significance level to test the author's claim that the results fit a uniform distribution. What does the result suggest about the ability of the four students to select the same tire when they really didn't have a flat?

Left Front=11, Right Front=15, Left Rear= 8, Right Rear=6

American Idol. The contestants on the TV show "American Idol" try to win a singing contest. At one point, the web site WhatNotToSing.com listed the actual numbers of eliminations for different orders of singing, and the expected number of eliminations was also listed. The results are in the table below. Use a 0.05 significance level to test the claim that the actual eliminations agree with the expected numbers. Does there appear to be support for the claim that the leadoff singers appear to be at a disadvantage?

Singing Order 1 2 3 4 5 6 7 thru 12
Eliminations 20 12 9 8 6 5 9
Expected 12.9 12.9 9.9 7.9 6.4 5.5 13.5
Eliminations
Section 11-3

Baseball Player Births. In his book "Outliners", author Malcolm Gladwell argues that more baseball players have birthdates in the months immediately following July 31, because that was the cutoff date for non-school baseball leagues. Here is a sample of frequency counts of months of birthdates of American-born major league baseball players starting with January: 387, 329, 366, 344, 336, 313, 313, 503, 421, 434, 398, and 371. Using a 0.05 significance level, is there sufficient evidence to warrant rejection of the claim that American born major league baseball players are born in different months with the same frequency? Do the sample values appear to support Gladwell's claim?