Question

Is this valid? Determine whether each of the following simulation designs is valid. Justify your answer.

(a) According to a recent survey, $50\%$ of people aged $13$ and older in the United States are addicted to email. To simulate choosing a random sample of

$20$people in this population and seeing how many of them are addicted to email, use a deck of cards. Shuffle the deck well, and then draw one card at a

time. A red card means that person is addicted to email; a black card means he isn’t. Continue until you have drawn $20$cards (without replacement) for the sample.

(b) A tennis player gets $95\%$of his second serves in play during practice (that is, the ball doesn’t go out of bounds). To simulate the player hitting $5$second serves, look at pairs of digits going across a row in Table D. If the number is between $00$and $94$, the service is in; numbers between $95$and $99$indicate that the service is out.

Short answer

Part (a) It isn't valid.

Part (b) It is valid.

Step-by-step solution

Part (a) Step 1. Given Information  

We must determine and justify the validity of each of the following simulation designs.

Part (a) Step 2. Concept Used    

A simulation is a technique for replicating random behaviour using a model that accurately reflects the situation, which is typically done with random numbers.

Part (a) Step 3. Explanation  

The simulation in the question isn't accurate. It is not valid because if the automobiles are not replaced, the chances of finding someone who is addicted to email are no longer $50\%$As a result, the replacement is required. If you draw a red card (addiction), for example, the next draw will have $25$red cards and $26$black cards, giving you a probability of $\frac{25}{25+26}=\frac{25}{51}=0.4902=49.02\%$And this isn't even half of it. As a result, the outcome.

Part (b) Step 1. Explanation    

The simulation in the question is accurate. It is legitimate since there are 95 possible outcomes ranging from $00$ to $94$ as well as five outcomes ranging from $95$ to $99$ As a result, the serve has a $95$ out of $100$ chance of being in, which translates to $95$ percent of the time. As a result, the simulation is correct.