# Statistic Assignment

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Questions

1. According to a physiologist, “A person’s resting pulse should be between 60 and 100 bpm.” Assume that pulse rates are normally distributed, and let X denote the pulse rate of a random person.
1. Explain how you would interpret the physiologist’s statement as the probability distribution function (pdf) of X. (Note: there is no single correct answer.)
2. The physiologist further says that a fit person’s resting pulse should be between 55 and 80 bpm. Based on your answer in Q1 (a), what percentage of people can be considered “fit”? Use R to compute this.
3. If n =400 people are randomly selected, what is the probability that more than half of them can be considered “fit”? Explain whether you can apply the central limit theorem (CLT) for this computation, and use R to compute the numerical answer.
1. Let us interpret the physiologist’s statement in Q1 (b) as “fit people have resting pulse rates lower than 80 bmp.” We are interested in determining whether university students are fit according to this statement.
1. Use the data from the 92 students to conduct a hypothesis test at 5% significance level. You must
• state/depict H 0  and H A  with respect to the unknown population parameter(s) of interest,
• use one sentence to explain how you apply the principle of “H 0  is the default winner in the absence of data” to the practical context of Q2(a),
• use R to compute the test statistic and P-value,
• state and justify any assumption(s) deemed necessary,
• declare whether you reject H 0,
• make a conclusion based on your declaration in the practical context of Q2(a).
2. Use R to compute a 90% confidence interval (CI) for the mean resting pulse rate of university students. State and justify any assumption(s) deemed necessary.
1. The physiologist further explains, “For a fit person, a mild physical activity should only raise the person’s pulse slightly, then as soon as the activity stops, the person’s heart rate returns quickly to nearly his/her resting pulse rate.” Note that our data do not include pulse rates while the students were on the treadmill.
1. We are interested in determining whether university students are fit according to this statement. Use the data from the 92 students to conduct a hypothesis test at 1% significance level; the test should be appropriate in the context of Q3 (a). You must
• state/depict H 0  and H A  with respect to the unknown population parameter(s) of interest,
• use one sentence to explain how you apply the principle of “H 0  is the default winner in the absence of data” to the practical context of Q3(a),
• use R to compute the test statistic and P-value,
• state and justify any assumption(s) deemed necessary,
• declare whether you reject H 0  ,
• make a conclusion based on your declaration in the practical context of Q3(a).
2. Based on these data, is there reason to be believe that the percentage of fit female university students differs from the percentage of fit male university students? Use the data from the 92 students to conduct a hypothesis test at 1% significance level; the test should be appropriate in the context of Q3(b). You must
• state/depict H 0  and H A  with respect to the unknown population parameter(s) of interest,
• use one sentence to explain how you apply the principle of “H 0  is the default winner in the absence of data” to the practical context of Q3(b),
• use R to compute the test statistic and P-value,
• state and justify any assumption(s) deemed necessary,
• declare whether you reject H 0 ,
• make a conclusion based on your declaration in the practical context of Q3(b).
3. We wish to compare the fitness level between university students who declare themselves as “neither active nor inactive (ACTIVITY=2)” and those who declare themselves as inactive (ACTIVITY=1). Use the data from the 92 students to conduct a hypothesis test at 20% significance level; the test should be appropriate in the context of Q3(c). You must
• state/depict H 0 and H A with respect to the unknown population parameter(s) of interest,
• use one sentence to explain how you apply the principle of “H 0 is the default winner in the absence of data” to the practical context of Q3(c),
• use R to compute the test statistic and P-value,
• state and justify any assumption(s) deemed necessary,
• declare whether you reject H 0 ,
• make a conclusion based on your declaration in the practical context of Q3(c).
2. Write a brief paragraph to
• discuss which of the various “definitions” of fitness from Q2-3 you prefer,
• explain how you can use these data from the 92 students in a hypothesis test to compare the fitness level between overweight students and non-overweight students attending university, based on your choice for the definition of “fitness” in the paragraph.
1. Write a brief paragraph to discuss whether the statistical analyses from Q1-4 legitimately refer to “university students” which is our population of interest.