Question

e average rushing totals for the 2014 NFL offensive players per game is 113.34 yards. A sample of the top 10 rushers is 130.5 yards with a standard deviation of 21.37. Test whether the sample is significantly greater than the claim using a .05.

Answer 1

Here we have n = 10, $\overline{x}$ = 130.5, s = 21.37

Claim : The average rushing total is 113.34 yards.

We need to test if sample is significantly greater than the claim.

The hypothesis are :

H0 : $\mu$ = 113.34 v/s H1 : $\mu$ > 113.34

As sample size is less than 30. We use t test statistic.

The test statistic is,

$t = \frac{\overline{x}-\mu }{s/\sqrt{n}}$

$=\frac{130.5-113.34}{21.37/\sqrt{10}}$

= 2.539

Here n =10, $\alpha$ = 0.05, df = n-1 = 10-1 = 9

The critical value :

$t_{1-\alpha ,df}=t_{1-0.05,9}=1.833$

Here calculated value of t > critical value of t.

Hence we reject null hypothesis.

Conclusion : There is sufficient evidence to conclude that the average rushing total for the 2014 offensive players per game is 113.34 yards.