Question

A simple random sample of 153 men from a normally distributed population results in a standard deviation of 10.9 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal​ range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.01 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per​ minute; see the technology output available below for this test. What do the results indicate about the effectiveness of using the range rule of thumb with the​ "normal range" from 60 to 100 beats per minute for estimating sigma in this​ case? What are the null and alternative​ hypotheses? H0​: H1​:

Answer 1

Null hypothesis,  pulse rates of men have a standard deviation equal to 10 beats per minute

An alternative hypothesis,  pulse rates of men have a standard deviation IS NOT equal to 10 beats per minute.

sigma^2= 100

n= 153 COUNT

s^2= 10.9^2 = 118.8100

alpha= 0.01

Chisq = (n-1)*s^2/sigma^2 = (153-1)*118.81/100 = 180.5912

Critical values:

chisq(a/2,n-1) = chisq(0.01/2,153-1) = CHIINV(1-0.01/2,153-1) = 110.8458

chisq(1-a/2,n-1) = chisq(1-0.01/2,153-1) = CHIINV(1-0.01,153-1) = 114.3997

Since chisq > chisq(1-a/2,n-1), i reject the null hypothesis at 1% level of significance and conclude that pulse rates of men have a standard deviation equal to 10 beats per minute

according to the range rule of thumb, the range is equal to 4 times the value of standard deviation. that is r = 4s, that is s = r/4

in this case, range = 100-60 = 40

s = 40/4 =10