The owner of a professional football team believes that the

The owner of a professional football team believes that the league has become more offense oriented since live years ago. To check his belief, 23 randomly selected games from one year\'s schedule were compared to 23 randomly selected games from the schedule five years later. Since more offense produces more offensive yards per game, the owner analyzed the following information on offensive construct a point estimate and a 90% confidence interval for mu_1 - mu_2, the difference in average offensive yards per game between the two years observed. Test, at the 10% level of significance. whether the data on offensive yards per game sufficient evidence to conclude, the game has been, more offens orinented

Solution

This is the comparison of paired test

H0: mu1-mu2 = 0

Ha: mu1-mu2<0

As sample size is small, t statistic can be used.

The mean of Group One minus Group Two equals -20.00
  90% confidence interval of this difference: From -42.34 to 2.34


  t = 1.8046
  df = 22
  standard error of difference = 11.083

p value = .042423.

The result is significant at p < .10.

Hence at 10% sign level, reject null hypothesis that two means are equal.

Group	Group One	Group Two
Mean	316.00	336.00
SD	40.00	35.00
SEM	8.34	7.30
N	23	23