Question

Customers arrive at a movie theater at the advertised movie time only to find that they have to sit through several previews and prepreview ads before the movie starts. Many complain that the time devoted to previews is too long (The Wall Street Journal, October 12, 2012). A preliminary sample conducted by The Wall Street Journal showed that the standard deviation of the amount of time devoted to previews was four minutes. Use that as a planning value for the standard deviation in answering the following questions. a. If we want to estimate the population mean time for previews at movie theaters with a margin of error of 75 seconds, what sample size should be used? Assume 95% confidence.

Answer 1

Answer:

a) sample size is 40

Step-by-step explanation:

(a)

$\sigma=4$ minutes

Margin of error, E is 75 seconds E=75/60= 1.25 minutes.

The level of significance $\alpha= 0.05$ for 95% level of significance

For 95% confidence interval $z_{\frac{\alpha}{2}}=1.96$ from standard deviation table

Sample size required, n

$n=\left (\frac{z_{\frac{\alpha}{2}}\cdot \sigma}{E} \right )^{2}=\left (\frac{1.96\cdot4}{75/60} \right )^{2}=39.337984$

Rounding off, n=40

Sample size =40

Keywords:

95% confidence, sample size, Wall Street Journal