Final answer:
The study to test the medical researcher's claim that smokers have higher pulse rates than non-smokers is a one-tailed two-sample Z-test. The standard deviations are known and the test is at the 6% significance level. The null hypothesis is that the mean pulse rate for smokers is less than or equal to that of non-smokers.
Step-by-step explanation:
The scenario presents a hypothesis test to compare the mean pulse rates of smokers and non-smokers using a random sample of each group. To evaluate the medical researcher's claim that smokers have a higher pulse rate than non-smokers, one would perform a two-sample Z-test since the standard deviations of the populations are known. The test is to be conducted at the 6% level of significance. The random variable here is the difference between the mean pulse rates of smokers and non-smokers. As the researcher believes that the pulse rate for smokers is larger (not just different), this would be a one-tailed test, specifically the right-tailed test.
To proceed with the hypothesis test, one would establish the following:
- Null Hypothesis (H0): μ1 - μ2 ≤ 0 (The mean pulse rate for smokers is less than or equal to that of non-smokers.)
- Alternative Hypothesis (H1): μ1 - μ2 > 0 (The mean pulse rate for smokers is greater than that of non-smokers.)
Using the sample data provided, we would calculate the test statistic using the Z distribution and compare it to the critical value corresponding to the 6% level of significance. If the test statistic is greater than the critical value, the null hypothesis can be rejected in support of the alternative hypothesis that smokers have a higher mean pulse rate.