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 two decimal places.

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

Step 4 of 5 : Make the decision for the hypothesis test: Reject Null Hypothesis or Fail to Reject Null Hypothesis

Step 5 of 5 : State the conclusion of the hypothesis test: There is sufficient evidence to support the claim or There is not sufficient evidence to support the claim.

PLEASE DO NOT ANSWER UNLESS YOU ARE CONFIDENT YOUR ANSWER WILL BE CORRECT.

Answer 1

Since , the population standard deviations are known.

Therefore , use Z-test for testing two means.

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 :

Hypothesis: Vs  

Step 2 of 5 :

The test statistic is ,

Step 3 of 5 :

The p-value is ,

p-value=

; From standard normal distribution table

Step 4 of 5 :

Decision : Here , p-value=0.0142< 0.05

Therefore , reject Ho.

Step 5 of 5 :

Conclusion : There is sufficient evidence to support the claim that the pulse rate for smokers and non-smokers is different.