Question

An instructor of a statistics course had students report data about themselves, including hand preference (left or right handed) and pulses rate (beats per minute). We will use these data to conduct a hypothesis test to answer the question "does mean pulse rate differ for left-handed students, as compared to right-handed students?"

A. What are the hypotheses for your test?

B. Do you have paired samples or independent samples?

Answer 1

A. The null and alternative hypothesis

where , and are mean pulse rate for left handed and right handed people respectively.

Note : Our research hypothesis is " does mean pulse rate differ between left handed  and right handed students." First we state the null hypothesis , H0 , which is the hypothesis of no difference. Thus in the null hypothesis , we say that there is no difference in mean pulse rate ( ) , and the alternative hypothesis is our research hypothesis . We can see that the alternative hypothesis is non directional, as our test to find out whether there is a difference.So the test is two tailed . We are not interested to know whose pulse rate is more . In that case the alternative hypothesis would have been ( mean pulse rate for left handed more than  right handed people) or (mean pulse rate for left handed less than  right handed people) . And the test would have been one tailed.

B. The data is for two independent samples : pulse rate of left handed people and pulse rate of right handed people. Thus we have independent samples .

Note : Independent sample t test also known as two sample t test is used to conduct the test.

Note : Paired samples are paired observations on the same set of subjects under two circumstances . For example weight of a set of individuals before and after a special diet . Then we perform paired sample t test.