From a random sample of 50 people, sitting pulse rates and standing pulse rates were measured for each person. A coin was flipped to determine whether the sitting or the standing pulse rate would be measured first. Let μsitting represent the mean sitting pulse rate in the population, μstanding represent the mean standing pulse rate of the population, and μd represent the mean difference between the sitting and standing (sitting – standing) pulse rates of the population. Which of the following represents an appropriate test and hypotheses to determine if there is a difference in mean pulse rates between sitting and standing in the population?1. A two-sample t-test withH0 : μsitting = μstandingHA : μsitting ≠ μstanding2. A two-sample t-test withH0 : μsitting = μstandingHA : μsitting < μstanding3. A matched-pairs t-test withH0 : μd = 0HA : μd ≠ 04. A matched-pairs t-test withH0 : μd = 0HA : μd < 0

The matched paired t-test is appropriate choice because the observations in the data are paired. The observations in the data are the calculated pulse rates of 50 persons while sitting and standing. For each person. sitting and standing pulse rates are measured and this indicates the before and after effect is measured. The before and after effect is measured through matched paired t test.

Also, an investigator wants to determine whether there is difference in mean pulse rates between sitting and standing in population. This indicates two tailed test. so, the hypotheses would be

Null hypotheses : μd = 0

Alternative hypotheses: μd ≠ 0.

Thus, situation indicates a matched-pairs t-test with H0 : μd = 0, HA : μd ≠ 0.

astha8579 astha8579 · Answer 2 · 2022-03-23T14:35:54+01:00

The option that represents an appropriate test and hypotheses to determine if there is a difference in mean pulse rates between sitting and standing in the population is: Option C: A matched-pairs t-test with [tex]H_0 : \mu_d = 0\\H_A : \mu_d \neq 0[/tex]

When do we use two-sample t-test?

The two-sample t-test is used to determine if two population means are equal.

When to use the matched pair t test ?

When there has to be done comparison between means of two sets of paired data, then we use matched pair t test.

How to form the hypotheses?

There are two hypotheses. First one is called null hypothesis and it is chosen such that it predicts nullity or no change in a thing. It is usually the hypothesis against which we do the test. The hypothesis which we put against null hypothesis is alternate hypothesis.

Null hypothesis is the one which researchers try to disprove.

For this case, we want to determine if there is a difference in mean pulse rates between sitting and standing in the population.

That is the reason why we will use matched pair t-test.

Where paired data is the pair of data obtained from each of those 50 people, the pair of data being sitting pulse rate and standing pulse rate.

Now, since we want to determine if there's any difference, so the null hypothesis will nullify the presence of any difference.

Thus, we get:

Null hypothesis = [tex]H_0: \mu_d = 0[/tex] (the difference between mean of sitting pulse rate and that of standing pulse rate is 0, therefore no difference).

This can be rewritten as: [tex]H_0: \mu_{\text{sitting}} = \mu_{\text{standing}}[/tex]

Alternate hypothesis = [tex]H_A: \mu_d \neq 0[/tex] or [tex]H_A: \mu_{\text{sitting}} \neq \mu_{\text{standing}}[/tex]

Thus, the option that represents an appropriate test and hypotheses to determine if there is a difference in mean pulse rates between sitting and standing in the population is: Option C: A matched-pairs t-test with [tex]H_0 : \mu_d = 0\\H_A : \mu_d \neq 0[/tex]

Learn more about matched pair t-test here:

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