Question

A simple random sample of 45 men from a normally distributed population results in a standard deviation of 12.6 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. a. Identify the null and alternative hypotheses. Choose the correct answer below. A. Upper H 0 : sigma equals 10 beats per minute Upper H 1 : sigma less than 10 beats per minute B. Upper H 0 : sigma not equals 10 beats per minute Upper H 1 : sigma equals 10 beats per minute C. Upper H 0 : sigma equals 10 beats per minute Upper H 1 : sigma not equals 10 beats per minute D. Upper H 0 : sigma greater than or equals 10 beats per minute Upper H 1 : sigma less than 10 beats per minute b. Compute the test statistic. chi squaredequals nothing ​(Round to three decimal places as​ needed.) c. Find the​ P-value. ​P-valueequals nothing ​(Round to four decimal places as​ needed.) d. State the conclusion. ▼ Reject Do not reject Upper H 0​, because the​ P-value is ▼ greater than less than or equal to the level of significance. There is ▼ sufficient insufficient evidence to warrant rejection of the claim that the standard deviation of​ men's pulse rates is equal to 10 beats

Answer 1

s = 12.6

n = 45

α = 0.10

a) Null and alternative hypothesis:

Hₒ : σ = 10

H₁ : σ ≠ 10

b) Test statistic:

χ² = (n-1)s² / σ² = (45 - 1)12.6² /10² = 69.854

c) Degree of freedom:

Df = n -1 = 45 - 1 = 44

p-value = CHISQ.DIST.RT(69.854, 44) = 0.0078

d) Decision:

p-value < α, Reject the null hypothesis.

Reject H0​, because the​ P-value is less than or equal to the level of significance. There is sufficient evidence to warrant rejection of the claim that the standard deviation of​ men's pulse rates is equal to 10 beats.