Question

A simple random sample of 35 men from a normally distributed population results in a standard deviation of 12.5 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.

Compute the test statistic .Find the​ P-value. State the conclusion.

Answer 1

Solution:

Given ,

n = 25

s = 12.5

Claim: = 10

Use = 0.10

Hypothesis can be written as

H0 :   =  10 vs H1 :   10

The test statistic is

² = (n - 1)s²/²

= (25 - 1) (12.5)²/(10²)

= 37.5

Test statistic ² = 37.5

Now , n = 25

So , d.f. = n -1 = 25 - 1 = 24

  sign in H1 indicates the TWO tailed test.

Test statistic ² = 37.5

Using calculator ,

p value = 0.077964

Since p value is less than = 0.10 ,

Reject the null hypothesis H₀

Conclusion : There is sufficient evidence to reject the claim that pulse rates of men have a standard deviation equal to 10 beats per minute.