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 85 percent confidence and an error of ± 5 percent (i.e. 0.05). What is the required sample size (to the next higher integer)?

Answer 1

Answer: 208

Explanation:

When prior estimate of population proportion is not available , then the formula for sample size:
`n=0.25((z^*)/(E))^2`

, wherez*= critical-value.

E= Margin of sampling error.

Let p be the population proportion of existing customers who would purchase a "digital upgrade" to their basic cable TV service.

As per given , we have

E= ± 5 percent= ± 0.05

Using z-table , the critical z-value corresponding to 85% confidence level = z*=1.439

Then, the required sample size :
`n=0.25((1.439)/(0.05))^2`

`\Rightarrow\ n=(0.25)(28.78)^2`

`\Rightarrow\ n=0.25(828.2884)\\\\\Rightarrow\ n=207.0721\approx208` [Rounded to next integer.]

Thus, the required sample size = 208