A manufacturing company wants to use a sample to estimate the proportion of defective tennis balls that are produced by a machine and the company wants the margin of error to be within 3% ( .03 ) of the population proportion of all defective tennis balls and to be 99% confident. There is no previous survey on this. What is the least number of tennis balls needed for the sample?

The least number of tennis balls needed for the sample is 1849.

Step-by-step explanation:

The (1 - α) % confidence interval for population proportion is:

The margin of error for this interval is:

Assume that the proportion of all defective tennis balls is p = 0.50.

The information provided is:

MOE = 0.03  

Confidence level = 99%

α = 1%

Compute the critical value of z for α = 1% as follows:

*Use a z-table.

Compute the sample size required as follows:

Thus, the least number of tennis balls needed for the sample is 1849.