Try Magic Notes and save time.Try it free
Try Magic Notes and save timeCrush your year with the magic of personalized studying.Try it free
Question

# Use the given data to find the minimum sample size required to estimate a population proportion or percentage. An investor is considering funding of a new video game. She wants to know the worldwide percentage of people who play video games, so a survey is being planned. How many people must be surveyed in order to be 90% confident that the estimated percentage is within three percentage points of the true population percentage? Assume that about 16% of people play video games (based on a report by Spil Games).

Solution

Verified
Step 1
1 of 2

Given:

$c=90\%=0.90$

$E=3\%=0.03$

$\hat{p}=16\%=0.16$

Formula sample size:

$\hat{p}\text{ known: }n=\dfrac{[z_{\alpha/2}]^2\hat{p}\hat{q}}{E^2}=\dfrac{[z_{\alpha/2}]^2\hat{p}(1-\hat{p})}{E^2}$

$\hat{p}\text{ unknown: }n=\dfrac{[z_{\alpha/2}]^2 0.25}{E^2}$

For confidence level $1-\alpha=0.90$, determine $z_{\alpha/2}=z_{0.05}$ using using the normal probability table in the appendix (look up 0.05 in the table, the z-score is then the found z-score with opposite sign):

$z_{\alpha/2}=1.645$

$\hat{p}$ is known, then the sample size is (round up to the nearest integer!):

$n=\dfrac{[z_{\alpha/2}]^2 \hat{p}(1-\hat{p})}{E^2}=\dfrac{1.645^2\times 0.16(1-0.16)}{0.03^2}\approx 405$

## Recommended textbook solutions #### Elementary Statistics

13th EditionISBN: 9780134462455 (1 more)Mario F. Triola
2,569 solutions #### Probability and Statistics for Engineers and Scientists

9th EditionISBN: 9780321629111 (9 more)Keying E. Ye, Raymond H. Myers, Ronald E. Walpole, Sharon L. Myers
1,204 solutions #### The Practice of Statistics for the AP Exam

5th EditionISBN: 9781464108730 (1 more)Daniel S. Yates, Daren S. Starnes, David Moore, Josh Tabor
2,433 solutions #### Statistics and Probability with Applications

3rd EditionISBN: 9781464122163Daren S. Starnes, Josh Tabor
2,555 solutions