Question

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)* Mean 23.7 16.4 11.9 Matchup 1 vs. 16 2 vs. 15 3 vs. 1 4 vs. 13 5 vs. 12 6 vs. 11 7 vs. 10 8 vs. 9 Number of Games 20 20 20 20 20 20 20 20 Variance 114.8 90.8 62.1 149.3 159.1 146.5 83.7 100.5 5.9 5.6 -0.7 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 2-seed and the 15-seed (2 vS. 15) Historically, the variance in the margins of victory for first-round 2 vs. 15 matchups has been σ2-130.0, (130.0 is the variance of the margins of victory for the 2 vs. 15 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).] Assume that the population of first-round victory margins is normally distributed and that the 20 games summarized in the table constitute a random sample of recent first-round games The statistics student should formulate the hypothesis test as: Ho: σ2 90.8, Ha: σ2 < 90.8 90.8, Hai σ2 > 90.8 O Ho: σ2 Ho: σ's 130.0, Hai σ2 > 130.0 Ho: σ2 130.0, Hai σ2 < 130.0 The value of the test statistic is

Answer 1

null hypothesis:     Ho:				σ2 =	130
Alternate hypothesis: Ha:				σ2 <	130

value of the test statistic X2=(n-1)*s2/σ2 =

13.271

rejection rule is :reject Ho if X2<=

11.651

the p value Is :

0.1756

Whether the statistics student uses the critical value approach or the p-value approach for the hypothesis test, the null hypothesis is not rejected ; the evidence provided by the sample data do not give conclusion that the variance of the margin of victory has declined. the