Question

A simple random sample of 34 men from a normally distributed population results in a standard deviation of 11.8 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 0.10 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.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: σ = 10
Alternative Hypothesis, Ha: σ ≠ 10

Rejection Region
This is two tailed test, for α = 0.1 and df = 33
Critical value of Χ^2 are 20.867 and 47.4
Hence reject H0 if Χ^2 < 20.867 or Χ^2 > 47.4

Test statistic,
Χ^2 = (n-1)*s^2/σ^2
Χ^2 = (34 - 1)*11.8^2/10^2
Χ^2 = 45.949

P-value Approach
P-value = 0.1329
As P-value >= 0.1, fail to reject null hypothesis.

There is not sufficient evidence to conclude that the pulse rates of men have a standard deviation not equal to 10 beats per minute.