Chapter 11.1, Problem 3E

To determine

To find which sample size has smallest margin of error.

Answer to Problem 3E

Sample size $50$ .

Explanation of Solution

Given:

The Pew Research Center recently conducted a survey of a random sample of $200$ teens and concluded that $43\%$ of all teens who take their cell phones to school text in class on a daily basis.

Calculation:

The following is the record of the percent of teens who text for each trial in the table given below:

Sample Size	1	2	3	4	5	6	7	8	9	10
20	28%	40%	30%	32%	45%	46%	48%	44%	38%	60%
50	78%	39%	48%	65%	49%	39%	68%	55%	27%	39%
100	42%	43%	44%	49%	38%	78%	79%	54%	67%	34%

The farthest point of sample size $20$ is $\begin{array}{l}60\%\hfill \end{array}$ .

Discarding it the range of remaining nine percent is maximum $-$ minimum $=48-28=20\%$

The farthest point of sample size $50$ is $\begin{array}{l}78\%\hfill \end{array}$ .

Discarding it the range of remaining nine percent is maximum $-$ minimum $=68-27=41\%$

The farthest point of sample size $100$ is $\begin{array}{l}79\%\hfill \end{array}$ .

Discarding it the range of remaining nine percent is maximum $-$ minimum $=78-34=44\%$

On observing the above, it can be concluded the sample size $50$ has smallest margin error.