Question

A nurse at a local hospital is interested in estimating the birth weight of infants. how large a sample must she select if she desires to be 95​% confident that the true mean is within 3 ounces of the sample​ mean? the population standard deviation of the birth weights is known to be 6 ounces.

a. 3
b. 4
c. 15
d. 16

Answer 1

The nurse must select a sample size of 16 to be 95% confident that the true mean is within 3 ounces of the sample mean.

Step-by-step explanation:

To calculate the sample size needed, we use the formula:

n = (Z * σ / E)^2

Where:

• n is the required sample size
• Z is the z-value corresponding to the desired level of confidence (in this case, 95% confidence, so Z = 1.96)
• σ is the population standard deviation (known to be 6 ounces)
• E is the desired margin of error (3 ounces)

Plugging in the values, we get:

n = (1.96 * 6 / 3)^2 = 15.69

Rounding up to the nearest whole number, the nurse must select a sample size of 16.