Answer to Question #167667 in Statistics and Probability for kienth bryan doroin

Question

A new sneaker claims that it can make male athletes jump higher. A sample of 69 male athletes is asked to jump once with their own sneakers on and once wearing the new sneakers. The average jump increased by 5.03 inches with the new sneakers with a standard deviation of 2.53 inch(es). Find the lower bound of a 95% confidence interval.

Answer 1

Solution

Let $\mu_1 =$ avg. jump with new sneakers

$\mu_2 =$ avg jump with own sneakers

$H_0 : \mu_1 - \mu_2 =0$ vs $H_1 : \mu_1 - \mu_2 >0$

Lower bound :

$$(\bar{x_1} - \bar {x_2}) - Z_{ \alpha } ({\sigma \over \sqrt {n}})$$

$$=5.03-1.64({2.53 \over \sqrt {69}})$$

=4.5305 inches