Chapter 5.1, Problem 15E

To determine

To find out whether the simulation design is valid or not.

Answer to Problem 15E

Yes, the design is valid.

Explanation of Solution

In this question a study of teens addicted to smartphones was considered. And the researcher finds out that the percentage was too high. Now, we are interested in simulating a random sample of size $100$ in which $50\%$ feel addicted to their devices and we are interested in estimating the probability that $40$ or less teens feel addicted. So, we have that,

  $\begin{array}{l}1=\text{ Feels addicted}\\ 2=\text{ Does not feel addicted}\end{array}$

Since we use a random number generator to produce $100$ random integers from $\text{1 to 2}$ and since $\text{1}$ corresponds with feels addicted this corresponds with a $\text{1 in 2}$ chance of obtaining an individual who feels addicted or equivalently $50\%$ .

Moreover, we estimate the probability as percentage of trials on which the number of $\text{1's was 40}$ or less and thus the simulation design is valid.