An experiment looks at the proportion of people who have played video games with

Question

An experiment looks at the proportion of people who have played video games within the last week. -if our experiment’s sample size increased, what would happen to the confidence intervals and probabilities given above? An experiment looks at the proportion of people who have played video games within the last week. -if our experiment’s sample size increased, what would happen to the confidence intervals and probabilities given above? -if our experiment’s sample size increased, what would happen to the confidence intervals and probabilities given above?

Explanation / Answer

The given distribution is binomial since it's values are either 1(played the video game) or 0 (did not play the video game).

Assuming that we are performing a normal approximation of this binomial distribution, as the sample size increases, the normal approximation becomes more and more representative of the actual binomial distribution. As a result, the error decreases and hence the width of confidence interval decreases, representing greater confidence in the results of our experiment. On similar lines, the probability function that estimates the proportion would become more accurate.

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