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**Unformatted text preview: **Fall 2000 Statistics 130 Midterm 1 Rein Instructions: ‘
0 Write your name on your exam book. Write your name on your formula sheet. You will need to turn both
in. Please keep your copy of this exam because it will be beneﬁcial to have it on hand when you look over
your graded work.
o Work independently. Ifyou would like me to rephrase any questions, just ask.
0 Each question is worth the same number of points. Sub-parts within each problem will each have about the
same number of points. 1. For this question please read the following news article from Monday October 9, 2000. Garlic: A Clove a Day May Keep Cancer at Bay NEW YORK (Reuters Health) - While legends have suggested that garlic has the
power to protect against evil, scientists have found a more practical reason for keeping the seasoning in stock. Eating a lot of garlic-—but not garlic
' supplements--seems to protect against stomach and colorectal cancer,
inVestigators report. Dr. Lenore Arab and colleagues from the University of North Carolina at Chapel
Hill analyzed 18 studies looking at garlic eaters. Their findings are published
in the October issue of the American Journal of Clinical Nutrition. The average intake of the highest consumers of raw or cooked garlic was 18.3
grams per week--approximate1y six cloves--with a range extending to more than
28.8 grams per week. Based on six studies, the findings suggest that "high consumption of raw or
cooked garlic decreases the risk of colorectal cancer from 10% to nearly 50%,"
the authors write. Based on four studies, the risk of developing stomach cancer
was cut in half for those who consumed the most garlic. Arab‘s group notes that the association was not consistent across all of the
studies. However, they did find that consumption of garlic supplements did not
decease cancer risk. The researchers caution that such studies are often hampered by problems
because they were not performed in a consistent manner and may have been
complicated by the consumption of other types of food-—such as vegetables--that
may have an impact on cancer risk. 7 For 8 points each answer the following: a. This research is an example of “meta analysis” where information from several studies is
lumped together to achieve a higher sample size. Can we conclude for sure whether the
studies were experiments or observational studies? What clues do we have that would
help us guess? b. Identify a confounding factor mentioned in the article. c. The research article in the American Journal of Clinical Nutrition mentioned that they
did not ﬁnd a statistically signiﬁcant relationship between garlic use and breast cancer.
Does that mean that using garlic, as a fact, does not affect the rate of breast cancer?
Explain. 2. I am trying to measure the heights of my kids. Suppose I have the choice of using two
measurement devices, an “inch stick” (1/36th of a yardstick), a tape measure that has been
stretched (so that the while the maximum distance indicated on the tape-measure is reads 60
inches it really is 62 inches). For 8 points each answer the following: a. Which of the two (the “inch stick” or the stretched tape measure) would give me a
reliable measurement of their heights? (Or would both or neither be reliable?)
b. Which of the two (or both or neither) would give me an unbiased measurement of their heights? 3. The last two times I taught Stat 130 were Spring
1999 and Fall 1999. At right is a histogram of
both classes scores taken together. Below at 20
right is a side-by-side boxplot of the scores E
shown broken down by quarter. The data g inl- summaries shown (below) were calculated with
MINITAB: Z) 30 40 50 I) TO 80 W 100 "0 Quarter N Mean Stande Deviation mam, S ring 1999 60 _71.5 14.6
al 19 6 75.4 12.8 Quarter an 40 50 I: 70 80 so 100 110 . M1 Score
For 8 pomts each: a. Is the distribution of scores in Fall 1999 approximately symmetrical? Which
information (graphical or numerical) helps us answer this question? b. Supposing that scores in Fall 1999 were, indeed, following a Normal curve, approximately what percentage of the students that term scored above 90 points on the exam? What is the 25"] percentile of midterm scores in Fall 1999? Can we approximately determine the value of the stande deviation of all the midterm scores (both groups taken together)? Approximately determine this value if possible (and be clear how you are doing so) or explain why it cannot be done. 9-? Fall 2000 Midterm 1 Rein 4. For 4 points each, match the histograms (AG) to the dataset (1-7) with the given summaries. Fall 2000 Midterm l Rein “A W 009‘! Statistics 130 Sample Midterm Two 1. “Type A” individuals are hard working and outgoing individuals. We also lmow that one’s level of education is not related to
whether one is “Type A” or not. Furthermore, we know: 40% of Americans are “Type A” individuals 70% of Americans graduate from High School 35% of Americans go to college 21% of Americans graduate from college 1% of Americans have some post-graduate education If we were to choose an adult American at random: (a) What is the chance that the selected individual is a college graduate?
(b) What is the chance that the individual is “Type A”?
(c) What percent of Americans who enroll in college eventually graduate?
(d) What is the chance that the individual is a “Type A” person who has not attended college?
- (e) What is the chance that the individual is either a college graduate or one who never graduated from High School? 2. On page A-30 of the Feb 13, 1997 New York Times there was an article by Gina Kolata entitled “First proof: driving while
talking on phone is a hazard” This article refers to a study in the New Engand Journal of Medicine, which looked at the rate of
cellular phone usage for drivers involved in accidents. Automobile drivers who had been involved in an accident during July 1994
and August 1995 in Toronto who also own a cell phone were sampled. 0f the 699 individuals who were included in the study,
phone records were checked for calls (incoming or outgoing) in the 10 minutes immediateiy preceding the accident and during a
control period of 10 minutes (the day before the accident). You may assume that this is a representative sample of drivers who
have had accidents and also have a cell phone. The data are as follows: Cell call during No cell call during
control u riod control Total W? Cell call before
accident
No call before
accident Total 699 3. Fill in the missing values in the above table. in Wt Is there evidence here to convince you that drivers talking on the phone are at a higher risk of auto accident? Why or why
not? 3. Answer Tme or False for 5 points each: (Maybe drawing a scatterplot for each problem will help you answer.) a. If two variables, x and y, have correlation 0.7, we can conclude that there is a linear relationship between x and y.
) if two variables, x and y, have a correlation of 0.7, we can conclude that 70 percent of the y’s are correlated with the x’s.
(c) Iftwo variables, x and y, have a correlation of 0.7, we could certainly predict a y-value with more accuracy if we
knew the x-valuethanifwe didn’t. j; Mde-e nmiWM WWW” (d) Iftwo variables, x and y, have a correlation of 0.0, we can say that there is no association between x and y.
(e) Iftwo numeric variables, x and y, have no association, the correlation between x and will be about 0.0.
can/er amm- linear 6155001 whim Wigwam Z mandates,
4. Answer part a for 15 points and part b for 10
a. Consider ﬂipping a coin exactly eight times
i. What is the chance of getting eight heads in a row when ﬂipping a coin exactly 8 times (IiHHI-II-II-II-II-I)?
ii. Is it more likely that you will get the exact series H'I‘I‘TH'I'I'H than eight heads in a row when ﬂipping a coin 8
times?
iii. What is the name for the commonly held belief about the relative likelihood of such events?
{it} If a rare genetic disorder occurs in one out of every 100,000 births and if a test for this disease has a false positive rate of 1%
\D and a false negative rate of 1% and if 2 million babies each year are given this test at birth:
i. What number will test positive for this disorder? 5. Rein N ﬂ ‘Mv‘fwﬁ
W What percent of those who test positive will actually have the disorder? 5. Farmer Brown has a magic farm. On this farm there are 150 animals, 50 cows, 50 pigs, 30 chickens and 20 ducks. Of course,
none of the cows can ﬂy. The 30 chickens also cannot ﬂy. All the ducks can ﬂy. However, because this is a magic farm, 25 of the
pigs have wings. But only 10 of the pigs with wings can ﬂy. a. If I randomly choose an animal from this farm, what is the chance that it has wings? b. I“ randomly choose an animal from this farm, what is the chance that it can ﬂy? c. IfI randomly choose an animal with wings ﬁ'om this farm, what is the chance that it can ﬂy?
d. IfI randomly choose one pig and one bird, what is the chance that both can ﬂy? 6. My father-in-law prides himself on growing tomatoes. Last year I managed to convince him to perform an experiment on his
tomato crop. For each of his ten tomato plants (all the same variety and growing in the same place in the yard) he applied a
diﬁerent amount of fertilizer. He then recorded the number of tomatoes he harvested oﬁ‘ of each plant, The correlation between
amount of fertilizer and number of tomatoes was 0.739 and the regression line predicting number of tomatoes from amount of fertilizer is:
Number of tomatoes = 50.7 + 0.782 fertilizer level. 55
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fertilizer level Predict, if reasomble, the number of tomatoes he would get off of a plant with fertilizer level 12. If not reasonable, explain h why not.
(‘0 MSW Predict, if reasonable, the number of tomatoes he would get off of a plant with fertilizer level 25. Ifnot reasonable, explain
why not.
VEL Ifthe plants that received no fertilizer and 15 units of fertilizer had not been in this experiment (suppose that he only used the
E?“ other fertilizer levels on eight plants) would the correlation between fertilizer level and number of tomatoes be higher, lower or about the same?
\‘a d. Is it possible that using fertilizer increases the number of tomatoes? Are you convinced that using fertilizer increases the
number of tomatoes? How much fertilizer would you suggest using, based on these data? 7. Answer each of the following questions brieﬂy. a. Explain how you could calibrate a weatherman’s predictions of rain (usually given in terms of chance of precipitation).
Research by Slovic and colleagues found that people judged that accidents and diseases cause about the same number of
deaths in the US, whereas in truth diseases cause about 16 times as many deaths as accidents. Explain why. 0. Suppose that you go to your doctor for a routine examination, without any complaints of problems. A blood test reveals that
you have tested positive for a certain disease. Which of the following do you need to know to assess how worried you should
be? (Identify all that apply.) The false positive rate, the false negative rate and the percent of the population with this disease. ma WWW W mammal m lounge nunwrlmM‘W
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