Because of the popularity of movies as an entertainment medium for college students,you plan to do a national study of the average cost of a movie ticket.If you assume that $\text { ? }$
= $0.50,what sample size would you have to take to be 95% confident that your estimate was within $0.25 of the true mean ticket prices?
A) 15
B) 7
C) 8
D) 4
E) 16

Question

Because of the popularity of movies as an entertainment medium for college students,you plan to do a national study of the average cost of a movie ticket.If you assume that $\text { ? }$
 = $0.50,what sample size would you have to take to be 95% confident that your estimate was within $0.25 of the true mean ticket prices?
A) 15
B) 7
C) 8
D) 4
E) 16

Quizplus · Accepted Answer

To find the required sample size for estimating the mean with a specific confidence level and margin of error, you can use the formula for the sample size of a mean: $n = \left(\frac{Z\sigma}{E}\right)^2$, where $Z$ is the Z-score corresponding to the desired confidence level (for 95% confidence, $Z = 1.96$), $\sigma$ is the population standard deviation, and $E$ is the margin of error. Plugging in the given values ($\sigma = 0.50$, $E = 0.25$), we get $n = \left(\frac{1.96 \times 0.50}{0.25}\right)^2 = \left(\frac{0.98}{0.25}\right)^2 = 3.84^2 = 14.75$. Since sample size must be a whole number, we round up to the nearest whole number, which is 16.

Because of the Popularity of Movies as an Entertainment Medium ? \text { ? } ?

Because of the Popularity of Movies as an Entertainment Medium $\text { ? }$