Chapter 7, Problem 7.88RE

To determine

To find: that is this convincing evidence that using drugs helped improve their performance.

Explanation of Solution

Given:

Probability of pitched is 0.5 of showing improvement without taking drugs

Formula used:

  $\text{Probability}\text{=}\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}$

Calculation:

Probability of pitched is 0.5 of showing improvement without taking drugs which means that 5 out of 10 times the pitcher does not improve.

Improve: Digits 0, 1, 2, 3, 4

Not improve: Digits 5, 6, 7, 8, 9

Using a TI-83 calculator do the simulation or using table B

Command is for 19 values:

  $randInt\left(0,9,19\right)$

Observed the number of pitchers out of 19 pitchers that showed improvement and repeating the simulation 100 times.

8, 9, 10, 9, 11, 8, 16, 7, 8, 9 ...9

4 out of the 100 values are 14

  $\begin{array}{c}\text{Probability}\text{=}\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}\\ =\frac{4}{100}\\ =0.04\end{array}$

Therefore the estimated probability is 0.04 (answer could vary)