Question

You are curious about the average number of yards Matthew Stafford throws for each game for the Detroit Lions. You randomly select 27 games and see that the average yards per game is 250.4 with a standard deviation of 32.45 yards. You want to create a 95% confidence interval for the true average number of yards per game he throws. What is the margin of error for this estimate

Answer 1

Answer:

Margin of Error = 10.712

Step-by-step explanation:

The provided information is:

Sample size, n = 27

Mean $(\bar{x})$ = 250.4

Standard deviation (s) = 32.45

Degree of freedom = n - 1 = 26

Level of significance = $\alpha = 0.05$

Then, Critical Value is:  $t_{\frac{\alpha}{2},df}=t_{0.025,26}=2.06$

Thus, Margin of Error:

$\begin{aligned}E &= t_{\frac{\alpha}{2},df}\times\frac{s}{\sqrt{n}}\\&=2.06\times \frac{32.45}{\sqrt{27}}\\&=2.06\times5.20\\&=10.712\end{aligned}$