Question

A medical researcher wants to compare the pulse rates of smokers and non-smokers. He believes that the pulse rate for smokers and non-smokers is different and wants to test this claim at the 0.05 level of significance. A sample of 72 smokers has a mean pulse rate of 75, and a sample of 81 non-smokers has a mean pulse rate of 72. The population standard deviation of the pulse rates is known to be 6 for smokers and 9 for non-smokers. Let μ1 be the true mean pulse rate for smokers and μ2 be the true mean pulse rate for non-smokers.

Step 1 of 5: State the null and alternative hypotheses for the test.

Step 2 of 5: Compute the value of the test statistic. Round your answer to 2 decimal places

Step 3 of 5: Find the p-value associated with the test static. Round your answer to 4 decimal places

Step 4 of 5: Make the decision for the hypothesis test

Step 5 of 5: State the conclusion of the hypothesis test (Sufficient evidence or not enough evidence)

Answer 1

For sample 1 :

x̅1 = 75, σ1 = 6, n1 = 72

For sample 2 :

x̅2 = 72, σ2 = 9, n2 = 81

α = 0.05

1) Null and Alternative hypothesis:

Ho : µ1 = µ2

H1 : µ1 ≠ µ2

2) Test statistic:

z = (x̅1 - x̅2)/√(σ1²/n1 + σ2²/n2 ) = (75 - 72)/√(6²/72 + 9²/81) = 2.4495

3) p-value :

p-value = 2*(1-NORM.S.DIST(ABS(2.4495, 1) = 0.0143

4) Decision:

p-value < α, Reject the null hypothesis

5) Conclusion:

There is enough evidence to conclude that the pulse rate for smokers and non-smokers is different at 0.05 significance level.