Question

Speed, size, and strength are thought to be important factors in football performance. The article "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 random sample of 33 starting players (various positions were represented) from Division I teams that were not ranked in the top 20 resulted in a sample mean weight 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 105, the known value for top-20 teams?

Answer 1

While we cannot confidently conduct a hypothesis test due to missing details, z-scores are a standard method to compare the weights of individuals relative to their teams. However, unit discrepancies prevent accurate comparisons between the California quarterback and Texas player without conversions.

Step-by-step explanation:

To address the question of whether there is sufficient evidence to conclude that the mean weight for non-top-20 starters is less than 105 kg, we would typically conduct a hypothesis test (one-sample t-test). However, since specific details about the level of significance and the exact hypothesis test process are missing in the provided information, we cannot confidently provide a complete answer regarding the evidence.

The number of standard deviations the most famous quarterback (who weighs 205 pounds) is from the mean can be found using a z-score calculation, which is (individual's weight - mean weight) / standard deviation. The z-score for the California quarterback (assuming the team's mean weight is 103.3 kg and standard deviation is 16.3 kg) can't be computed because the quarterback's weight is given in pounds and we do not have a conversion factor here to kg.

To determine who was lighter, the California quarterback or the Texas player, we can compare their z-scores. Again, since we have a discrepancy in units (pounds vs kilograms) for the California quarterback, we cannot confidently compute which player is lighter without proper conversion.

Answer 2

no

Step-by-step explanation:

H0: mean of sample=105

Ha: mean of sampe≠ 105

t-statistic= (population mean-sample mean)/(standard deviation/√sample size)

t-statistic= (105-103.3)/(16.3/√33)

t-statistic= 0.5991

degress of freedom= 32

for alpha 0.05, p-value from t-distributino table is 1.697

since t-statistic is less than the p-value, null hypothesis is accepted.

There is no sufficient evidence to conclude that the mean weight for non-top-20 starters is less than 105 the known value for top-20 teams