Question

A health care professional wishes to estimate the birth weights of infants. How large a sample she needs to select if she desires to be 95% confident that the true mean is within 3 (+/-3 gms) of the sample mean? The standard deviation of the birth weights is known to be 105 gms.

Answer 1

Answer on Question #49372 – Math – Statistics and Probability

A health care professional wishes to estimate the birth weights of infants. How large a sample she needs to select if she desires to be 95% confident that the true mean is within 3 (+/-3 gms) of the sample mean? The standard deviation of the birth weights is known to be 105 gms.

Solution

The sample size is given by the formula:

$$n = \left(\frac {z ^ {*} \sigma}{E}\right) ^ {2},$$

where $z^{*} = 1.96$ at 95% confidence level, $\sigma = 105$ gms is the standard deviation of the birth weights,

$E = 3$ gms is the margin of error.

So,

$$n = \left(\frac {1.96 \cdot 105}{3}\right) ^ {2} = 4706 \text{ when rounded up}.$$

Answer: 4706.

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