The pulse rates of 166 randomly selected adult males vary from a low

Question

The pulse rates of 166 randomly selected adult males vary from a low of 45 bpm to a high of 109 bpm. Find the minimum sample size required to estimate the mean pulse rate of adult males. Assume that we want ​98% 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=enter your response here

​(Round up to the nearest whole number as​ needed.)

Answer 1

The mean pulse rate of males varies from a low 45 bpm to a high 109 bpm.

Therefore, the range of pulse rate is as follows.

Range =109-45=64.

The range rule allows us to quickly estimate the standard deviation of a sample, σ. The standard deviation is approximately equal to the range of the data divided by 4. 

σ= 64/4=16

The sample size can then be calculated by substituting the values of zα/2, σ, and E into the formula

n= [((zα/2)*σ)/E]²

Since you are told that the confidence interval is 98%, α=0.02 and α/2=0.01. You don’t actually have to look up zα/2 in a z-table every time. For most hypothesis tests, you’ll probably be using one of four confidence levels (90%, 95%, 98% and 99%). The z alpha/2 for each confidence level is always the same; for a 98% confidence level, zα/2 is 2.326.

Since you are told that the sample mean is within 2 bpm of the population mean, this means that the margin of error, E, is 2.

You will get your answer when you substitute all the above values into the formula I bolded previously. Also, I wrote my answer assuming that you were familiar with the content needed to solve this question but please let me know if you would like a more thorough explanation of what all these statistics mean.

Hope this helps!