Question

A marketing firm is asked to estimate the percent of existing customers who would purchase a "digital upgrade" to their basic cable TV service. The firm wants 99 percent confidence and an error of ± 5 percent. What is the required sample size (to the next higher integer)?A. 664B. 625C. 801D. 957

Answer 1

Answer: A. 664

Explanation:

Given : A marketing firm is asked to estimate the percent of existing customers who would purchase a "digital upgrade" to their basic cable TV service.

But there is no information regarding the population proportion is mentioned.

Formula to find the samples size , if the prior estimate to the population proportion is unknown :

`n=0.25((z*)/(E))^2`

, where E = Margin of error.

z* = Two -tailed critical z-value

We know that critical value for 99% confidence interval =
`z*=2.576` [By z-table]

Margin of error = 0.05

Then, the minimum sample size would become :

`n=0.25((2.576)/(0.05))^2`

Simplify,

`n=0.25*2654.3104=663.5776\approx664`

Thus, the required sample size= 664

Hence, the correct answer is A. 664.