Question

A simple random sample of pulse rates of 20 women from a normally distributed population results in a standard deviation of 12.2beats 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

The statistical software output for this problem is:

One sample variance summary hypothesis test:

σ² : Variance of population
H₀ : σ² = 100
H_A : σ² ≠ 100

Hypothesis test results:

Variance	Sample Var.	DF	Chi-square Stat	P-value
σ2	148.84	19	28.2796	0.1564

Hence,

a) Hypotheses:

H₀ : σ = 10
H_A : σ ≠ 10

b) Test statistic = 28.280

c) P - value = 0.156

d) Since p - value is greater than 0.01,we do not reject Ho. Hence,

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