ANSWER THE FOLLOWING QUESTIONS:
It is suspected that among fraternal twins, the first-born
twin has a higher resting heart rate from ages 0-2 years. The Excel sheet
provided by your instructor contains resting heart rate data (in beats per
minute) 129 pairs of randomly selected fraternal twins, measured at age 1 year.
Answer the following, furnishing relevant calculations and explanations where
appropriate:
(1)
a.
Write two to three sentences discussing the most
appropriate type of experimental design and sampling strategy for this
experiment.
b.
Suppose that the data set in this experiment was
not provided to you, how would you judge what sample size to collect?
(2)
a.
What type of inferential test would be
appropriate in this situation? Be sure to include valid statistical
justification and discuss both confidence interval estimation and hypothesis
testing in your response.
b.
Discuss the appropriate confidence and
significance levels. How did you calculate these values?
(3)
a.
State the formal null and alternative for your
hypothesis test determined in part (2) using symbolic form. Make sure to use
correct notation.
b.
State the formal null and alternative for your
hypothesis test in words.
(4)
Using the Excel sample data, complete the
relevant hypothesis calculations.
a.
Include an Excel screenshot showing the summary
statistics relevant to this hypothesis test.
b.
Furnish an Excel screenshot from the master
template, clearly highlighting the test-statistic, p-value, and any other
information you deem relevant.
(5)
Make a formal decision on the null hypothesis.
a.
State your decision in formal statistical
language.
b.
State your decision using language relevant to
the application discussed (resting heart rate difference between the twins).
(6)
Using the Excel sample data, complete the
relevant confidence interval calculations.
a.
Furnish an Excel screenshot clearly highlighting
the confidence level, lower limit, and upper limit, as well as any other
information you deem relevant.
b.
Is zero in your confidence interval? Explain why
this is important to note.
(7)
Discuss the implication of the confidence
interval.
a.
Does the confidence interval suggest the same
decision on the null as (6)? Explain how you arrived at your answer in detail.
b.
Discuss what the confidence interval tells us
about the difference between the twins’ heart rates at age 1 year.
(8)
If the sample size were increased to n=1290, 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? Explain in
detail.
(9)
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?
OTHER INFORMATION:
It is suspected that among fraternal twins, the first-born
twin has a higher resting heart rate from ages 0-2 years. The attached Excel
sheet contains resting heart rate data (in beats per minute) 129 pairs of randomly
selected fraternal twins, measured at age 1 year. Answer the following,
furnishing relevant calculations and explanations where appropriate:
(1)
Determine the most appropriate type of
experimental design and sampling strategy for this experiment. Note you are not
collecting the actual data, as the sample is provided, but describe how this
data set could be collected in the most accurate and unbiased way.
(2)
What type of inferential test would be
appropriate in this situation? Be sure to include valid statistical
justification and discuss both confidence interval estimation and hypothesis
testing in your response. Discuss the appropriate confidence and significance
levels.
(3)
State the formal null and alternative for your
hypothesis test determined in part (2). Make sure to use correct notation.
(4)
Using the attached Excel sample data, complete
the relevant hypothesis calculations. Furnish an Excel screenshot clearly
highlighting the test-statistic, p-value, and any other information you deem
relevant.
(5)
Make a formal decision on the null hypothesis.
State your decision both in formal statistical language and using language
relevant to the application discussed (resting heart rate difference between
the twins).
(6)
Using the attached Excel sample data, complete
the relevant confidence interval calculations. Furnish an Excel screenshot
clearly highlighting the confidence level, lower limit, and upper limit, as
well as any other information you deem relevant.
(7)
Discuss the implication of the confidence
interval. Does the confidence interval suggest the same decision on the null as
(6)? Explain how you arrived at your answer in detail. Discuss what the
confidence interval tells us about the difference between the twins’ heart
rates at age 1 year.
(8)
If the sample size were increased to n=1290, 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? Explain in
detail.
(9)
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?
