Chapter 5.2, Problem 5.53E

(a)

To determine

To show that the margin of error quoted in the question is approximately correct if a simple random sample is taken.

Answer to Problem 5.53E

  $1.8\%$

Explanation of Solution

If a simple random sample is taken, then the margin of error is as;

  $\begin{array}{l}\text{ME=}\frac{1}{\sqrt{n}}\\ \text{ME=}\frac{1}{\sqrt{3024}}\approx 1.8\%\end{array}$

(b)

To determine

To make an approximate statement about video gaming in the population of American adults.

Explanation of Solution

We are $95\%$ confident that the true population of adults who play computer or video games is between $38\%\text{ and 42\%}$ .

(c)

To determine

To identify two possible error in this question that margin of error does not include.

Answer to Problem 5.53E

Some adults may have lied about whether or not they play video games.

Some adults did not report playing a video game.

Explanation of Solution

One source of error may have been that some adults may have lied about whether or not they play video games. Another source of error may be that some adults did not report playing a video game because they did not consider the game they were playing to be a video game.

To determine

(d)

To explain if this survey is repeated today, then the result would be about the same or not and do some research about our suspicion is correct or not,

Answer to Problem 5.53E

It will increase.

Explanation of Solution

This proportion would likely have increased because of the popularity of smartphones and the ease at which games can be downloaded on smartphones.