A simple random sample of 42 men from a normally distributed population results

Question

A simple random sample of 42 men from a normally distributed population results in a standard deviation of 11.1 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 0.05 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute. Complete parts (a) through (d) below. a. Identify the null and alternative hypotheses. Choose the correct answer below. O B. Ho: = 10 beats per minute H1 : #10 beats per minute 0 D. Ho: = 10 beats per minute H1 :

Explanation / Answer

a)
Null and alternate hypotheis are as per Option B where we want to test the claim whether pulse rates of men have a standard deviation equal to 10 beats per minute.

b)
Test statistics, chi-square = (N-1)*(s/sigma)^2

Here n = 42, s = 11.1
sigma = 10

chi-square = (42 -1)*(11.1/10)^2 = 50.5161

c)
df = 42 - 1 = 41

This is two tailed test
p-value = 0.2931 (=2*CHISQ.DIST.RT(I14,41))

FAil to reject the null hypothesis as p-value is greater than the significance level of 0.05.
this means there are not significant evidence to conclude that mean pulse rate of men is different from 10 beats per minute.

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