7. Hypothesis testing about a population variance Summary statistics for the first-round games in the five National Collegiate Athletic Association (NCAA) basketball tournaments between 2004 and 2008 are displayed as follows: Margin of Victory (Points)* Matchup Number of Games Mean Variance 1 vs. 16 20 23.7 114.8 2 vs. 15 20 16.4 90.8 3 vs. 14 20 11.9 62.1 4 vs. 13 20 9.1 149.3 5 vs. 12 20 5.9 159.1 6 vs. 11 20 5.6 146.5 7 vs. 10 20 6.1 83.7 8 vs. 9 20 -0.7 100.5 *The margin of victory is negative for an upset (a win by the lower-seeded team). (Data source: These calculations were obtained from data compiled by The News & Observer.) The NCAA tournament is divided into four regions; 16 teams, seeded 1 to 16, are assigned to each region. In the first round of tournament play, in each of the four regions, the 1-seed plays the 16-seed, the 2-seed plays the 15-seed, and so on. As a result, in each tournament, there are four opening-round games for each matchup. A college basketball fan (who is also a statistics student) hypothesizes that for a given matchup the margins of victory in the first-round games are more consistent (as measured by their variance) in recent tournaments than in past tournaments. She decides to conduct a hypothesis test for the matchup between the 3-seed and the 14-seed (3 vs. 14). Historically, the variance in the margins of victory for first-round 3 vs. 14 matchups has been of = 144.0. (144.0 is the variance of the margins of victory for the 3 vs. 14 matchup in first-round tournament games played from 1985 to 1997.) [Source: H. S. Stern and B. Mock, "College Basketball Upsets: Will a 16-Seed Ever Beat a 1-Seed?" Chance 11, no. 1, (1998).]The statistics student conducts the hypothesis test using a level of significance of a = 0.01. Use the Distributions tool to find the critical value that marks the border of the rejection region. According to the rejection region method, you: O Reject Ho if x2 6 7.633 O Reject Ho if F $ 0.330 O Reject Ho if F 2 3.027 O Reject Ho if x2 2 7.633 O Reject Ho if x- 2 36.191 Now use the tool to find the p-value. The p-value is Whether the statistics student uses the rejection region method or the p-value approach for the hypothesis test, the null hypothesis ; the evidence provided by the sample data the conclusion that the variance of the margin of victory has declined