Statistics

Statistics
) In this problem, some headlines are shown. Indicate whether the statement is one of association and causation, association only, or neither.

a) Daily exercise improves mental performance.
b) Among college students, no connection found between number of friends on social networking websites and size of the university.
c) Wealthy people are more likely to be heavy-set compared to less-wealthy people.
e) Cream with green tea extract hinders HIV transmission.
f) Lack of insurance to blame for 45,000 deaths per year.
2. (4pts) A study published in 2010 showed that city dwellers have a 21% higher risk of developing anxiety disorders and a 39% risk of developing mood disorders than those who live in the country. A follow-up study published in 2011 used brain scans of city dwellers and country dwellers as they took a difficult math test. To increase the stress of the participants, those conducting the study tried to humiliate the participants by telling them how poorly they were doing on the test. The brain scans showed very different levels of activity in stress centers of the brain, with the urban dwellers having greater brain activity than rural dwellers in areas that react to stress.

a) Can we conclude from the 2010 study that living in a city increases a person’s likelihood of developing an anxiety disorder or mood disorder? Explain.
b) Can we conclude from the 2011 study that living in a city increases activity in stress centers of the brain when a person is under stress? Explain.

3. (4pts) An advertisement makes the claim: “Lighter shoes make you run faster.” Of the following, which is the best way to investigate this claim?
a) Choose the records of the top twenty runners who are wearing the lighter shoes and compare their times to run 400 meters before and after they began wearing the shoes.
b) Choose twenty runners and select ten at random to wear lighter shoes and have the other ten wear heavier shoes to run 400 meters and compare their times.
c) Choose twenty runners at random and have the women wear the lighter shoes and the men wear the heavier shoes to run 400 meters and compare their times.
d) Choose to observe the results of 400-meter races for the next year and see how many winners are wearing the lighter shoes.

Explain the reasoning behind your choice.
4. (4pts) Which of the following plans would be the best way to collect data to determine if listening to music while studying for a social studies exam has an effect on exam performance?
a) Randomly select a sample of students enrolled in a social studies class. After an exam in that class, ask each of these students the following two questions: (1) Did you listen to music while studying for the exam? and (2) What score did you get on the exam?
b) Survey every student enrolled in a social studies class. After an exam in that class, ask each of these students the following two questions: (1) Did you listen to music while studying for the exam? and (2) What score did you get on the exam?
c) Use a group of student volunteers who are enrolled in a social studies class. Randomly assign each student to either the music group or the no music group. Students in the music group will listen to music while studying for an upcoming exam and those in the no music group will not listen to music while studying for this exam. Record the exam score for each student.
d) Use a group of students who are all enrolled in a social studies class. Have each student volunteer for either the music group or the no music group. Students in the music group will listen to music while studying for an upcoming exam and those in the no music group will not listen to music while studying for this exam. Record the exam score for each student.
Explain the reasoning for your choice.
5. (5pts) To estimate the proportion of Americans who support changing the drinking age from 21 to 18, a random sample of 100 college students are asked the question “Would you support a measure to lower the drinking age from 21 to 18?”
a) What is the population of interest?
b) What is the parameter of interest?
c) What is the sample?
d) What is the statistic?
e) Will the statistic under-, over-, or well-estimate the parameter of interest?
6. (5pts) To estimate the proportion of Americans who would be interested in a new type of ice skate, a random sample of 1500 Minnesotans are asked about their interest in the product.
a) What is the population of interest?
b) What is the parameter of interest?
c) What is the sample?
d) What is the statistic?
e) Will the statistic under- or over-estimate the parameter of interest? Explain.

7. (8pts) Forced expiratory volume (FEV) measures the amount of air you can exhale in 1 second. FEV is often used as a measure of lung capacity. The FEV data set contains FEV (measured in liters per second) along with age, sex, smoking status, and height for 654 children and teens.
a. (4pts) Describe the association between FEV and smoking status. Your response should include a graphical display that is clear and easy to interpret (and you should interpret it!). You may also include numeric summaries to aid in your response. What, if anything, is surprising about this association?
b. (4pts) What other single variable in the data set might be confounding the relationship between smoking status and FEV, and help explain the surprising result from part a)? Describe how this confounding might be occurring.
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