Question

Smartphone addiction? A media report claims that $50\%$of U.S. teens with smartphones feel addicted to their devices. A skeptical researcher believes that this figure is too high. She decides to test the claim by taking a random sample of $100$U.S. teens who have smartphones. Only $40$of the teens in the sample feel addicted to their devices. Does this result give convincing evidence that the media report’s $50\%$claim is too high? To find out, we want to perform a simulation to estimate the probability of getting $40$or fewer teens who feel addicted to their devices in a random sample of size $100$from a very large population of teens with smartphones in which 50% feel addicted to their devices.

Let $1$= feels addicted and $2$= doesn’t feel addicted. Use a random number generator to produce $100$random integers from $1$to $2$. Record the number of $1$’s in the simulated random sample. Repeat this process many, many times. Find the percent of trials on which the number of $1$’s was$40$ or less.

Short answer

We utilise a random number generator to generate $100$random integers from $1$to $2$and since $1$equates to feeling hooked, we have a $1$in$2$ probability of finding someone who feels addicted, or a chance of finding someone who feels addicted.

Step-by-step solution

Given Information

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

Simplification

A study of teenagers addicted to cellphones was used to answer this topic. And the researcher discovers that the proportion was incorrectly calculated. Now, we want to simulate a random sample of size $100$in which $50\%$of the teens are addicted to their devices, and we want to estimate the likelihood that $40$or fewer teens are addicted. So there you have it.

$1$= Feels addicted

2 = Does not feel addicted

Since we utilise a random number generator to generate $100$random integers from $1$to $2$and since $1$equates to feeling hooked, we have a $1$in $2$probability of finding someone who feels addicted, or a $50\%$chance of finding someone who feels addicted.

Furthermore, we calculate the probability as a percentage of trials with $1$'s of $40$or less, indicating that the simulation design is valid.