Question

1. Speed, size and strength are thought to be important factors in football performance. The paper “Physical and Performance Characteristics of NCAA Division I Football Players” (Research Quarterly for Exercise and Sport (1990): 395-401) reported on physical characteristics of Division I starting football players in the 1988 football season. Information for teams ranked in the top 20 was easily obtained, and it was reported that the mean weight of starters on top-20 teams was 105 kg. A sample of 23 starting players (various positions were represented) from Division I teams that were not ranked in the top 20 resulted in a sample mean of 103.3 kg and a sample standard deviation of 16.3 kg. Is there sufficient evidence to conclude that the mean weight for non-top-20 starters is less than the known value for top-20 teams? Conduct hypothesis test using α=.0

Answer 1

Data given:
n = 23, y = 103.3, s = 16.3, u0 = 105, a = 0.01;

Step 1 - State the Hypotheses:
     Ho: u = 105
     Ha: u < 105

Step 2 - State the Test Statistic:
     t = (y-u0)/(s/root(n))

Step 3 - State the Critical or Rejection Region:
The critical region depends upon Ha.

For t < 105, we reject Ho if
     t < - tn-1,a
     t < - t(22,0.01)
     t < -2.508

Step 4 - Conduct Experiment and Calculate Test Statistic:
     t = (y-u0)/(s/root(n))
     t = (103.3-105)/(16.3/root(23))
     t = -0.5

Step 5 - Reach Conclusions and State in English:
Since it is not true that t < -2.508, we don't have sufficient evidence to reject Ho. We therefore accept that the true mean is not less than 105.