You suspect that among fraternal twins born across the United States, the second-born twin has a higher resting heart rate from ages 0-

MAT-274 Inferential Statistics Project

You suspect that among fraternal twins born across the United States, the second-born twin has a higher resting heart rate from ages 0-2 years. Your instructor will provide an Excel sheet containing resting heart rate data (in beats per minute) for 129 pairs of fraternal twins, measured at age 1 year. You will be addressing the following areas, including relevant calculations and explanations; see the assignment style guide for details about what to consider in your responses:

(1) Consider how your data is obtained.

(2) Select an appropriate hypothesis test.

(3) Describe your hypothesis in mathematical and nonmathematical terms.

(4) Using your Excel sample data, complete the relevant hypothesis test calculations.

(5) Make a formal decision on your null hypothesis.

(6) Using your Excel sample data, complete the relevant confidence interval calculations.

(7) Discuss how to interpret your confidence interval.

(8) Consider the effects of increasing the sample size.

(9) Consider confounding variables.

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MAT-274 Inferential Statistics Project Style Guide

You suspect that among fraternal twins born across the United States, the second-born twin has a higher resting heart rate from ages 0-2 years. Your instructor will provide an Excel sheet containing resting heart rate data (in beats per minute) for 129 pairs of fraternal twins, measured at age 1 year. Answer the following, including relevant calculations and explanations as indicated:

(1) Consider how your data is obtained.

a. Suppose the twin data were not provided to you and that you had to collect the data yourself. Discuss an appropriate experimental design and sampling strategy for this data. If you were collecting the data, how would you go about ensuring that it is truly representative of twins across the U.S.? Also discuss why it might be interesting to consider fraternal rather than identical twins.

b. Similarly, if the data were not provided, discuss how you would determine the sample size to collect. More specifically, if you were not able to assume Normally distributed data, how much larger might your sample size need to be to obtain the same confidence interval width as you would have with Normally distributed data and 129 data points? Explain how the underlying distribution affects the sample size.

(2) Select an appropriate hypothesis test.

a. Given that you have pairs of twin data, and that each pair of twins shares an environment makes the pair’s characteristics likely to be closer to each other than to those of other twin pairs, what type of inferential test is appropriate for this case? (Note: there is a specific test that is most appropriate here.) In your response, also select a different incorrect test and explain why the test you chose is correct and this second test is incorrect, in terms of the likely accuracy of your confidence interval and hypothesis testing.

b. You will test your hypothesis at the 0.05 level of significance and construct a 95% confidence interval. Explain why these selections are reasonable. Also explain why it is generally crucial to fix these selections before you start testing; that is, what is theoretically wrong with looking at the data before you decide on a specific hypothesis, level of significance, or confidence interval?

(3) Describe your hypothesis in mathematical and nonmathematical terms.

a. State, in mathematical notation, the null hypothesis and alternative hypothesis for the hypothesis test represented by the statement at the beginning of this document. Use appropriate notation.

b. State, in words, the null hypothesis and alternative hypothesis for the same test; use complete sentences with correct grammar and syntax.

(4) Using your Excel sample data, complete the relevant hypothesis test calculations.

a. Summarize your results here, including the calculation of any relevant means, standard deviations, test statistics, p-value calculations, degrees of freedom, critical values, decision procedures, and any other inputs or calculations you used to perform the test. (Note: this should be text and not a screenshot. If you’d like, you can use the equations editor in Word.)

b. Also include an Excel screenshot showing your calculations. Note that you should omit any extraneous inputs or calculations.

(5) Make a formal decision on your null hypothesis.

a. State your decision in formal statistical language; in your statement, you should repeat your null and alternative hypotheses and include the significance level you used.

b. Translate your decision into an interpretation of the result relevant to the application (resting heart rate difference between the twins); use complete sentences with correct grammar and syntax.

(6) Using your Excel sample data, complete the relevant confidence interval calculations.

a. Summarize your results here, including the calculation of any relevant means, standard deviations, number of data points, degrees of freedom, confidence interval bounds, and any other inputs or calculations you used to derive your confidence interval. (Note: this should be text and not a screenshot. If you’d like, you can use the equations editor in Word.)

b. Is the value 0 inside or outside of your confidence interval? Explain what it would mean for the value 0 to be inside your confidence interval.

(7) Discuss how to interpret your confidence interval.

a. Discuss in detail what your confidence interval tells us about the difference in the twins’ heart rates at age 1 year. Specifically, provide a statement that would inform a lay reader how to interpret the lower bound and upper bound of your confidence interval in the context of the question of whether the second-born twin has a higher resting heart rate.

b. Does your confidence interval suggest the same result as the conclusion you presented in question 5 above? Explain in detail why this is not surprising. Comment by Wayne Purdin (GCE): There is a decision and interpretation in Question 5 but no conclusion.

(8) Consider the effects of increasing the sample size: If the sample size were increased to n=1,290, but the pattern in the data continued, what would you expect to happen to the decision on the null? Would your decision be likely to change? Here, discuss in detail what tends to happen to any sample standard deviation, test statistic, and confidence interval as the sample size increases (keeping the significance level constant), and how this may lead to either the same result (strengthening your conclusion) or to a different result (changing your conclusion). For your data and conclusion, would increasing the sample size tend to strengthen or change your conclusion?

(9) Consider confounding variables: Finally, list at least three possible confounding variables that may cause this experiment to be biased or untrustworthy. How could you modify the experiment to control for these issues? (Here, you might consider different factors that could skew the sample data one way or another, from innate and environmental factors affecting pairs of fraternal twins to issues with data sampling or measurement protocols.)

© 2024. Grand Canyon University. All Rights Reserved.

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