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: A. 664Step-by-step 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 :[tex]n=0.25(\dfrac{z*}{E})^2[/tex], where E = Margin of error.z* = Two -tailed critical z-value We know that critical value for 99% confidence interval = [tex]z*=2.576[/tex]  [By z-table]Margin of error = 0.05Then, the minimum sample size would become :[tex]n=0.25(\dfrac{2.576}{0.05})^2[/tex]Simplify,[tex]n=0.25\times2654.3104=663.5776\approx664[/tex]Thus, the required sample size= 664Hence, the correct answer is A. 664.