Answer to Question #212655 in Statistics and Probability for mumine yarar

Question

The distance a basketball player runs during a game is one of the many variables used for assessing the performance of the players. 79 players are followed for a game each and the average distance ran by them is found to be 3457 meters (m) with a standard deviation of 147 m. Then the lower limit for the 95% confidence interval for the true mean is 

Answer 1

The critical value for $\alpha=0.05$ and $df=n-1=79-1=78$  degrees of freedom is $t_c=z_{1-\alpha/2, n-1}=1.990847.$  

The corresponding confidence interval is computed as shown below:

$$CI=(\bar{x}-t_c\times\dfrac{s}{\sqrt{n}}, \bar{x}+t_c\times\dfrac{s}{\sqrt{n}})$$

$$=(3457-1.990847\times\dfrac{147}{\sqrt{79}}, 3457+1.990847\times\dfrac{147}{\sqrt{79}})$$

$$=(3424.074, 3489.926)$$

The lower limit for the 95% confidence interval for the true mean is 3424.074 m.