Question

A scientist studying babies born prematurely would like to obtain an estimate for the mean birth weight,

μ, of babies born during the 24th week of the gestation period. She plans to select a random sample of birth weights of such babies and use the mean of the sample to estimate μ. Assuming that the population of birth weights of babies born during the 24th week has a standard deviation of 2.5 pounds, what is the minimum sample size needed for the scientist to be 99% confident that her estimate is within 0.6 pounds of μ?

Answer 1

To find the minimum sample size needed for the scientist to be 99% confident that her estimate is within 0.6 pounds of μ, use the formula n = ((Z * σ) / E)^2, where n is the sample size, Z is the z-score, σ is the population standard deviation, and E is the margin of error.

Step-by-step explanation:

To find the minimum sample size needed for the scientist to be 99% confident that her estimate is within 0.6 pounds of μ, we can use the formula:

n = ((Z * σ) / E)^2

where n is the sample size, Z is the z-score corresponding to the desired confidence level (in this case, 99%), σ is the population standard deviation, and E is the desired margin of error (in this case, 0.6 pounds).

Plugging in the values, we have:

n = ((2.576 * 2.5) / 0.6)^2 = 57.43

Therefore, the minimum sample size needed for the scientist to be 99% confident that her estimate is within 0.6 pounds of μ is 58 (rounded up to the nearest whole number).