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Exam 2
Math 104
Fall 2015
Myers
For full credit, please show all of the steps necessary to arrive at your answers.
You may use scratch paper to work out your responses, and then write them
neatly in the spaces provided here. You may use a calculator or GeoGebra and
two 3.5 x 5 inch notecards.
1. Fill in the blanks.
(a) The area under the normal curve between -1 and + 1 is about
(b) The area under the normal curve between -2 and +2 is about
(c) The area under the normal curve between -3 and +3 is about
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2. When should you not use r to summarize the relationship between two
variables?
3. What is the regression fallacy?
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4. Why do you have to be careful when interpreting ecological correlations?
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football-shaped. Predict the percentile rank on the final for a student whose
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between hours sp,ent per we~k doing homework, an~ sc,oreson,:~st~haii~aj~ed
achievement tests. The investigators concluded that doing homework helps
prepa,re students
thes~ tests. Does the con~lusiori.:'toilow fiom t~'e,d~~ir,
Answer yes or no, and explain, briefly.
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8. True or false: A student who is at the 40th percentile of first-year GPAs is
also likely to be at the 40th percentile of second-year GPAs. Explain briefly.
(The scatter diagram is football-shaped.)
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10. A gambler plays roulette 1,000 times. There are two possibilities:
(i) Betting $1 on a column each time.
(ii) Betting $1 on a number each time.
A column pays 2 to 1, and there are 12 chances in 38 to win; a number pays
35 to 1, and there is 1 chance in 38 to win.
(a) What is the gambler's expected net gain for option (i)?
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11. Consider the GeoGebra output below for the variables x = weight (in
pounds) and y = height (in inches).
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(a) Find the regression line for yon x.
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