Resting Heart Rate Hypothesis Test Assignment Guide

The brief hands you two methods and treats them as interchangeable, and they are not. You may either run a two-sample test with unequal variances or compare the two confidence intervals — but those two routes disagree in a specific, well-documented way, and the disagreement is almost certainly what the assignment is probing. Two confidence intervals that do not overlap guarantee a significant difference. Two that *do* overlap guarantee nothing: a difference can be significant at the conventional level while the intervals visibly overlap. So the comparison-of-intervals method can only ever confirm significance, never rule it out, and reporting "the intervals overlap, so there is no difference" is a real error rather than a shortcut. So decide which route you are taking before you look at the numbers, because the interval method can only support one of the two conclusions you might reach.

That is why the brief adds the sentence it does: we are looking for whether the difference is a significant one, not just whether they are not the same. Two sample means computed from real data will essentially never be identical, so observing that they differ is not a finding. The question is whether a difference of that size, with those sample sizes and those spreads, is larger than sampling variation comfortably explains. Answering the question the brief warns against — describing the gap between the two means and calling it a difference — is the single commonest way this assignment loses marks, and it is a conceptual failure rather than an arithmetic one, so the numbers being right will not rescue it. The distinction also tells you what the concluding sentence has to say: something about whether sampling variation can account for the gap, not about how big the gap looks.

Write the null hypothesis first, because the brief asks for it as a step and because it disciplines everything after it. The null here is that the two population means are equal — the mean resting heart rate of males equals that of females — with the alternative that they are not equal, which makes this a two-tailed test unless you have a directional reason and state it in advance. Write both hypotheses in symbols and in words, and make sure they are about population parameters rather than about your sample. A null written as "the sample means are equal" is testing something you can already see is false, and markers notice that particular slip because it reveals the misunderstanding underneath. State the significance level here too rather than at the end, since a decision rule chosen after seeing the p-value is not a decision rule.

The unequal-variances instruction is not incidental. The two-sample test with unequal variances — Welch's — does not assume the two groups share a common variance, and it is the safer default even when the variances look similar, because the pooled alternative loses accuracy quickly when they are not. In Excel's Data Analysis tool it is the option labelled t-Test: Two-Sample Assuming Unequal Variances. Choosing the equal-variance test instead, without testing or arguing for that assumption, is a decision you would have to defend. Following the brief and using unequal variances requires no defence at all, which is the practical reason to do what it says. Note in passing that the unequal-variance test reports fractional degrees of freedom, which is expected rather than an error, and reproducing that figure as your software gives it is part of reporting the test honestly.

Interpretation is the step where marks are actually available, and it needs three things rather than one. Report the test statistic, the degrees of freedom and the p-value; state the decision about the null in terms of the significance level you adopted; and then say what that means about resting heart rate in plain language. A p-value is the probability of data at least this extreme if the null were true — it is not the probability the null is true, and it is not a measure of how large the difference is. Keeping those separate is what distinguishes an interpretation from a restatement of the software output. Write this paragraph in sentences about heart rate, and let the numbers sit inside them, because a section that reads as a list of statistics has reported the analysis without interpreting it.

Report the effect, not just the verdict. Give the two sample means, the difference between them in beats per minute, and ideally a confidence interval for that difference, because a reader wants to know how much the groups differ and not only whether the difference cleared a threshold. With a class-sized dataset a real difference can easily fail to reach significance, and "we did not detect a significant difference" is an honest conclusion where "there is no difference" is not. Sample size drives that distinction, so noting how many males and how many females your data contains costs one sentence and shows you understand what the test can and cannot establish. A confidence interval for the difference does both jobs at once: it carries the test's verdict in whether it contains zero, and the effect size in where its endpoints sit.

The data is your own class heart rate data, which has consequences worth acknowledging briefly. Resting heart rate measured by students on themselves carries measurement error, the group is not a random sample of any population, and "resting" may mean different things to different people in the sample. None of that invalidates the exercise — it is exactly the situation applied statistics is usually in — but a sentence naming the limitation is the difference between a student who ran a procedure and one who understands what the result licenses. Physiological literature reports a genuine sex difference in resting heart rate, so an unexpected result is more likely to be about your sample than about physiology. Say that explicitly if your result runs the other way, because a student who notices the tension between their finding and the literature is demonstrating exactly the judgement the exercise is for.

The formatting requirements are explicit and separately checkable, so treat them as a checklist rather than as advice. The document is typed in a word processor and formatted in APA style, with a running head and a title page carrying the assignment name, your name and your professor's name. Paste the actual output — the Data Analysis table or the two confidence intervals — rather than only your summary of it, because the brief asks you to run the analysis and the output is the evidence you did. Label anything you paste so the reader knows which group is which, since an unlabelled two-column table forces the marker to guess which mean belongs to whom. Keep the output and the interpretation adjacent rather than banishing the tables to an appendix, since a marker reading the interpretation wants the numbers it refers to in view.