Question

An advertising company wishes to estimate the population mean of the distribution of hours of television watched per household per day. Suppose that the population standard deviation of hours watched per household per day is known to be 2.8 hours. The company decides that it wants the 99% confidence interval for the population mean to be no longer than 0.5 (hour). What is the minimum sample size that will result in a small enough confidence interval?

Answer 1

Answer: 208

Step-by-step explanation:

Given : An advertising company wishes to estimate the population mean of the distribution of hours of television watched per household per day.

Standard deviation : $2.8\text{ hours}$

Margin of error : $\pm0.5\text{ hour}$

Significance level : $\alpha=1-0.99=0.01$

Critical value : $z_{\alpha/2}=2.576$

The formula to calculate the sample size is given by :-

$n=(\dfrac{z_{\alpha/2}\sigma}{E})^2$

$\Rightarrow\ n=(\dfrac{2.576\times2.8}{0.5})^2=208.09793536\approx208$

Hence, the minimum required sample size must be 208.