Question

Simulation blunders Explain what’s wrong with each of the following simulation designs.

(a) According to the Centers for Disease Control and Prevention, about $26\%$of U.S. adults were obese in $2008$. To simulate choosing $8$adults at random and seeing how many are obese, we could use two digits. Let $01$to $26$represent obese and $27$to $00$represents not obese. Move across a row in Table D, two digits at a time, until you find 8 distinct numbers (no repeats). Record the number of obese people selected.

(b) Assume that the probability of a newborn being a boy is $0.5$. To simulate choosing a random sample of $9$babies who were born at a local hospital today and observing their gender, use one digit. Use ran dint (0,9) on your calculator to determine how many babies in the sample are male.

Short answer

Part (a) The Simulation is incorrect.

Part (b) In the Simulation, they're almost correct.

Step-by-step solution

Part (a) Step 1. Given Information 

The simulation designs are available for download. It is necessary to determine what is wrong with each of them.

Part (a) Step 2. Concept Used   

We can't foresee the outcomes of a chance process, yet they have a regular distribution over a large number of repetitions. According to the law of large numbers, the fraction of times a specific event occurs in numerous repetitions approaches a single number. The likelihood of a chance outcome is its long-run relative frequency. A probability is a number between $0$ (never happens) and $1$ (happens frequently) (always occurs).

Part (a) Step 3. Explanation    

Looking at the question's stimuli, we can conclude that repeats should be permitted in this simulation because if you don't, the probability of $26\%$ for obesity will no longer be accurate after the first two-digit number. As a result, the repeats are missing in this simulation, indicating that something is wrong with it.

Part (b) Step 1. Explanation   

We can deduce from the simulation provided in the question that the command $randlnt(0,9)$means that a number between $0$ and $9$ would be picked at random, and hence digits $0$ and $9$ are all equally likely to be drawn. Receiving four males in a sample of nine newborns, on the other hand, should not be significantly more likely than obtaining zero boys.