Question

Lefties A website claims that $10\%$of U.S. adults are left-handed. A researcher believes that this figure is too low. She decides to test this claim by taking a random sample of $20$U.S. adults and recording how many are left-handed. Four of the adults in the sample are left-handed. Does this result give convincing evidence that the website’s $10\%$claim is too low? To find out, we want to perform a simulation to estimate the probability of getting $4$or more left-handed people in a random sample of size $20$from a very large population in which $10\%$of the people are left-handed.

Let $00$to $09$indicate left-handed and $10$to 99 represent right-handed. Move left to Page Number: $311$right across a row in Table $D$. Each pair of digits represents one person. Keep going until you get$20$ different pairs of digits. Record how many people in the simulated sample are left-handed. Repeat this process many, many times. Find the proportion of trials in which$4$ or more people in the simulated sample were left-handed.

Short answer

We are selecting$20$ distinct pairs of digits, the simulation design is invalid because we are less likely to select a left-handed person after a left-handed person has been selected and more likely to select a left-handed person after a right-handed person has been selected.

Step-by-step solution

Given information

We have to find out whether the simulation design is valid or not.

Simplification

A research was done to determine how many people in the United States are left-handed. As a result, the researcher believes that the percentage obtained is quite low. As a result, we're interested in replicating a random sample of size $20$with $10\%$left-handedness and evaluating the likelihood that $4$or more people are left-handed. As a result,

$00$to $09$= Left handed

$10$to $99$= Right handed

Now, since we used a random number generator to generate $20$distinct pairs of digits, and since $00$to $09$corresponds to left-handed, this amounts to a $10$in $100$chance of getting a left-handed individual, or equivalently $10\%$.

However, because we are selecting $20$distinct pairs of digits, the simulation design is invalid because we are less likely to select a left-handed person after a left-handed person has been selected and more likely to select a left-handed person after a right-handed person has been selected.