Question

A research scholar wants to know how many times per hour a certain strand of virus reproduces. He wants to construct the 99% confidence interval with a maximum error of 0.18 reproductions per hour. Assuming that the mean is 5.7 reproductions and the variance is known to be 5.29, what is the minimum sample size required for the estimate?

Answer 1

To find the minimum sample size required for creating a 99% confidence interval with a maximum error of 0.18, the formula involving the z-value, known variance, and maximum error is used.

Step-by-step explanation:

The question poses a mathematical problem related to statistics, specifically confidence intervals and sample size determination. The research scholar wants to calculate a 99% confidence interval for the average number of times a virus reproduces per hour, with a maximum error of 0.18 and a known variance of 5.29. Given a mean reproduction rate of 5.7 per hour, we can use the formula for the minimum sample size:

n = (Z^2 * σ^2) / E^2,

where Z is the z-value corresponding to the 99% confidence level, σ^2 is the population variance, and E is the maximum error tolerance.

First, we identify the z-value for 99% confidence, which is approximately 2.576. We then plug in the variance and the maximum error to get:

n = (2.576^2 * 5.29) / 0.18^2.

Calculating this yields the minimum sample size required for the estimate.