Chapter 5.1, Problem 16E

To determine

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

Answer to Problem 16E

No, this design is not valid.

Explanation of Solution

In the question a study was conducted to find out how many of the people in U.S. are left-handers. Thus the researcher claims that percentage came out is very low. So, we are interested in simulating a random sample of size $20$ in which $10\%$ are left-handed and we are interested in estimating the probability that $4$ or more are left-handed. Thus, we have,

  $\begin{array}{l}00\text{ to 09}=\text{ Left handed}\\ \text{10 to 99}=\text{ Right handed}\end{array}$

Now, since we use a random number generator to produce $20$ different pairs of digits and since $\text{00 to 09}$ corresponds with left-handed, this corresponds with a $\text{10 in 100}$ chance of obtaining an individual who is left-handed or equivalently $10\%$ .

However, the simulation design is then not valid because we are selecting $20$ different pairs of digits and thus we are less likely to select a left-handed person after a left-handed person was selected and thus we are more likely to select a left-handed person after a right-handed person was selected.