Question

A pharmaceutical company advertises that a new type of beta blocker drug is just as effective as a pacemaker to regulate heart rates (in BPM). A group of clinicians finds it hard to believe, saying that no drug will ever be as reliable as a pacemaker when it comes to regulating heart rates.

A sample of 31 people that are given the new beta blocker drug is compared to a sample of 21people that already have pacemakers. We compute the sample variance of those taking the drug to be 29 BPM, while the sample variance of those with pacemakers is computed to be 8.

At a significance level of α=0.025 α = 0.025 , test the clinicians' claim that the variance in bpm from using beta blockers will be higher than the variance in bpm from a pacemaker.

(a) State the null and alternative hypotheses:

Answer 1

The null hypothesis is that the variance in heart rates from using beta blockers is not higher than the variance in heart rates from a pacemaker. The alternative hypothesis is that the variance in heart rates from using beta blockers is higher than the variance in heart rates from a pacemaker. To test these hypotheses, we compare the variances using the F-statistic and a significance level of 0.025.

Step-by-step explanation:

The null hypothesis is that the variance in heart rates from using beta blockers is not higher than the variance in heart rates from a pacemaker. The alternative hypothesis is that the variance in heart rates from using beta blockers is higher than the variance in heart rates from a pacemaker.

To test these hypotheses, we need to compare the variances of the two samples. The test statistic we will use is the F-statistic, which compares the ratio of the sample variances.

We can calculate the F-statistic using the formula:

F = (sample variance of beta blockers) / (sample variance of pacemakers)

Using the given sample variances, the F-statistic is:

F = 29 / 8 = 3.625

Next, we need to compare the F-statistic to the critical value from the F-distribution table at a significance level of 0.025. If the F-statistic is greater than the critical value, we reject the null hypothesis and conclude that the variance in heart rates from using beta blockers is higher than the variance in heart rates from a pacemaker.