Question

A simple random sample of pulse rates of 60 women from a normally distributed population results in a standard deviation of 12.7 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 women 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 = 0.01 and df = 59
Critical value of Χ^2 are 34.77 and 90.715
Hence reject H0 if Χ^2 < 34.77 or Χ^2 > 90.715

Test statistic,
Χ^2 = (n-1)*s^2/σ^2
Χ^2 = (60 - 1)*12.7^2/10^2
Χ^2 = 95.161

P-value Approach
P-value = 0.004
As P-value < 0.01, reject the null hypothesis.