Question

the pulse rates of 151 randomly selected adult males vary from a low of 36 bpm to a high of 104 bpm. find the minimum sample size required to estimate the mean pulse rate of adult males. assume that we want 99% confidence that the sample mean is within 2 bpm of the population mean. complete parts (a) through (c) below.
a. find the sample size using the range rule of thumb to estimate σ.
n = 480
(round up to the nearest whole number as needed.)
b. assume that σ = 12.5 bpm, based on the value s = 12.5 bpm from the sample of 151 male pulse rates.
n = 260
(round up to the nearest whole number as needed.)
c. compare the results from parts (a) and (b). which result is likely to be better?
the result from part (a) is the result from part (b). the result from is likely to be better because

Explanation:

Step1: Analyze the sample size relationship

The sample size \(n\) calculated using the range rule of thumb (part a) is \(480\), and the sample size \(n\) calculated using the sample standard deviation (part b) is \(260\). So, \(480>260\), which means the result from part (a) is larger than the result from part (b).

Step2: Determine the better - result criterion

When estimating the population standard deviation \(\sigma\), using the sample standard deviation \(s\) (as in part b) is a more accurate estimate than using the range rule of thumb (which is a very rough estimate: \(\sigma\approx\frac{\text{Range}}{4}\)). A more accurate estimate of \(\sigma\) leads to a more reliable sample size calculation for estimating the population mean.

Answer:

The result from part (a) is larger than the result from part (b). The result from part (b) is likely to be better because the sample standard deviation \(s = 12.5\) (used in part b) is a more accurate estimate of \(\sigma\) than the estimate of \(\sigma\) using the range rule of thumb (used in part a).