If we wanted to be 95 percent confident that we wouldn't make an error of more than 1 unit in our estimate of $\mu$ or $\sigma$= 2), we would need a sample size of approximately 16.

Question

Quizplus · Accepted Answer

This is correct based on the formula for calculating sample size for a 95% confidence interval with a margin of error of 1 unit (assuming normal distribution). The formula is:

n = (z * σ / E)^2

where n is the sample size, z is the z-score for the desired confidence level (1.96 for 95%), σ is the population standard deviation (in this case, we are given σ = 2), and E is the desired margin of error (in this case, E = 1).

Plugging in the values, we get:

n = (1.96 * 2 / 1)^2
n = 15.3664

Rounding up to the nearest whole number, we get n = 16. Therefore, we would need a sample size of approximately 16 to be 95% confident that we wouldn't make an error of more than 1 unit in our estimate of the population mean or standard deviation.

If We Wanted to Be 95 Percent Confident That We μ\muμ

If We Wanted to Be 95 Percent Confident That We $\mu$