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 0.01 level of significance. The researcher checks 39 smokers and finds that they have a mean pulse rate of 88, and 40 non-smokers have a mean pulse rate of 85. The standard deviation of the pulse rates is found to be 7 for smokers and 9 for non-smokers. Let My be the true mean pulse rate for smokers and uz be the true mean pulse rate for non-smokers. Step 1 of 4: State the null and alternative hypotheses for the test.

Step 2 of 4:

Compute the value of the test statistic. Round your answer to two decimal places.

Step 3 of 4:

Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to three decimal places.

Step 4 of 4:

Make the decision for the hypothesis test.

Answer 1

Step 1 of 4: Null hypothesis: H:44 = 42 That is, the pulse rate for smokers and non-smokers is same. Alternative hypothesis: H:47 That is, the pulse rate for smokers and non-smokers is different. Step 2 of 4: Excel add-in (PH Stat) procedure: Step 1: In EXCEL, Select Add-InsPH Stat>Two-Sample Tests (Summarized Data). Step 2: Choose Z test for Difference in Two Means. Step 3: In Data enter 0 Under Hypothesized Difference. Step 4: Enter 0.01 Under Level of Significance.

Step 5: In Population 1 Sample, enter Sample size as 39. Sample Mean as 88, and Sample Standard deviation as 7. Step 6: In Population 2 Sample, enter Sample size as 40. Sample Mean as 85, and Sample Standard deviation as 9. Step 7: Choose Two-Tail Test Under Test Options. Step 8: Click OK Excel add-in (PH Stat) output: Z Test for Differences in Two Means Data Hypothesized Difference Level of significance Population 1 Sample Sample Size Sample Mean Population Standard Deviation Population 2 Sample Sample Size Sample Mean Population Standard Deviation

Intermediate Calculations Difference in Sample Means Standard Error of the Difference in Means Z-Test Statistic 1.8115 1.6561 Two-Tail Test Lower Critical Value Upper Critical Value p-Value Do not reject the null hypothesis -2.5758 2.5758 0.0977 The value of the test statistic is Z=1.66. Step 3 of 4: Decision rule: If Z > Zçrit (= 2.576)or Z <Z«: (=-2.576), then reject the null hypothesis. Step 4 of 4:

Since Zcae (=1.66) < Zert (= 2.576), then do not reject the null hypothesis. Therefore, the pulse rate for smokers and non-smokers is same.