A health care professional wishes to estimate the birth weights of infants. The standard deviation of the birth weights is known to be 8 ounces. How large a sample must she select if she desires to be 95% confident that the true mean is within 6 ounces of the sample mean?

at least 6

Please send me this answer.

To determine the sample size needed, we can use the formula for sample size estimation:

n = (Z * σ / E)^2

Where:
n = sample size
Z = Z-score corresponding to the desired confidence level
σ = standard deviation
E = margin of error

In this case, the standard deviation is known to be 8 ounces, and the desired margin of error is 6 ounces. The confidence level desired is 95%, which corresponds to a Z-score of 1.96.

Plugging these values into the formula:

n = (1.96 * 8 / 6)^2
n = (1.96 * 1.333)^2
n = (2.61)^2
n = 6.8121

Since the sample size must be a whole number, the calculated sample size is rounded up to 7.

Therefore, the health care professional should select a sample size of at least 7 to be 95% confident that the true mean is within 6 ounces of the sample mean.

To determine the sample size needed to estimate the birth weights with a desired level of confidence, we can use the formula for the sample size needed for a confidence interval for a population mean.

The formula to calculate the sample size is:

n = (Z * σ / E)²

Where:
n = sample size
Z = Z-score corresponding to the desired confidence level (in this case, for a 95% confidence level, Z ≈ 1.96)
σ = standard deviation
E = margin of error (the distance from the sample mean to the desired true mean)

In this case, we want the true mean to be within 6 ounces of the sample mean, so E = 6 ounces.

Using the given information, let's plug in the values into the formula:

n = (1.96 * 8 / 6)²

n = (1.96 * 8 / 6)²
n ≈ 5.17²
n ≈ 26.78

Since we can't have a fraction of a sample, we must round up to the nearest whole number. Therefore, the healthcare professional must select a sample size of at least 27 infants to be 95% confident that the true mean is within 6 ounces of the sample mean.