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**Unformatted text preview: **Student ID: Print Name: Stat 217, Winter 2005 Exam 1 (Ver. A) Instructor: Dr. Jimmy Doi
m This is a closed book, closed notes examination. The use of a calculator is permitted.
Including this page, the exam has a total of 5 pages. There are a total of 12 questions. There are 100 points possible on this exam. Provide all answers on this exam and show all work
where appropriate. If necessary, you may use the back of these pages if you need more space. If you have any questions at all during the exam, please do not hesitate to come up and ask. Best
wishes and good luck! Read and sign the following before you submit the exam: By signing below, I understand that giving or receiving help on this exam is a
violation of academic regulations and is punishable by a grade of in the
course and possible further action by Cal Poly Judicial Affairs. Acts of violation
include revealing (actively or passively) any information about the exam to any
member of Prof. Doi’s Stat 217 class who is currently taking or not yettaken the exam. By signing below, I pledge not to violate academic regulations. Signature: Question 0: MAKE SURE YOUR NAME APPEARS ON THE FRONT OF THIS EXAM. Question 1: A television station is interested in predicting whether or not voters are in favor of an
increase in the state sales tax. It asks its viewers to phone in and indicate whether they support
or are opposed to an increase in the state sales tax in order to generate additional revenue for
education. Of the 2633 viewers who phone in, 1474 (55.98%) are opposed to the increase. The
population of interest is 11 people who will vote on the sales tax increase on the day of the vote. (b) all regular viewers of the television station who own a phone and have participated in similar
phone surveys in the past. (0) the 2633 viewers who phoned in. (d) the 1474 viewers who were opposed to the increase. Question 2: Given data on two quantitative variables X and Y, if the coefﬁcient of determination (T2) is equal to 1, then the slope of the least squares regression line ﬁt to this data must b
positive. Circle one: [True] l [False] 3 (1de be either
.be (“Elder ore-D Question 3: In all density curves, the median is less than or equal to the mean. Circle one: [we] Question 4: Let g} = a + be be the least squares regression equation for a set of data based on
variables X and Y. Let r be the correlation between X and Y for this data. If r > 0, then a > 0. Circle one: [True] Question 5: A small college has 500 male and 600 female undergraduates. A simple random sample
of 50 of the male undergraduates is selected, and, separately, 3 simple random sample of 60 of the
female undergraduates is selected. The two samples are combined to give an overall sample of 110
students. The overall sample is M a simple random sample. sail J12) Dc. ‘ a stratiﬁed random sample. - 0S2,ng exist ; Cameo-Hm L) g— 9“qu
£23" a multistage sample. I
(d) all of the above, Question 6: The following is a boxplot of the birthweights (in ounces) of a sample of 160 infants
born in a local hospital. 110 120 130 Wain»! {an anneal
100 (a) The median birthweight is approximately A) 80 B) 100 @110 D) 120 / (b) About 40 of the birthweights are below
\ 62
/
A) 92 102 C) 112 D) 120
(c) The range of the data is approximately
leo— Ema?
A) 130 B) 110 (3)350 D) 80 Question 7: The deciles of any distribution are the points that mark off the lowest 10% and highest
10%. On a density curve, these are the points with areas 0.1 and 0.9 to their left under the curve. What are the deciles of the standard normal distribution? Question 8: According to the Environmental Protection Agency (EPA), chloroform, which in its
gaseous form is suspected of being a cancer causing agent, is present in small quantities in all of our
country’s lakes. Suppose researchers at the EPA collected data by visiting each lake and measuring
its chloroform level. Here, the individuals of interest are the lakes and the variable of interest is
chloroform level. Researchers estimate the distribution of the amount of chloroform present among lakes to be nor-
mally distributed with mean and standard deviation 31.6 and 7.9 micrograms per liter, respectively. Find the proportion of lakes that have a chloroform level that is greater than 45 micrograms per
liter. Show all work to receive full credit. Khoc‘v \
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9643
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was: x>LFa= 1—965: .OLEE
W>w “15% Question 9: Measuring the rate of ﬂow of water in a stream requires specialized equipment. How—
ever, measuring the depth of a stream is relatively simple. A scientist would like to be able to use
a measurement of stream depth to predict the rate of ﬂow. She measures depth (m) and ﬂow rate (liter/sec) at diﬂ'erent points in several streams. Below are some summary values of the scientist’s data. _
25.9 (a) What are the explanatory angespon e variables?
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resetrﬁfa - 1% \ouD (b) Find the equation of the least squares regression line. (Show all work to receive full credit.) " , __ .9;
LS grow b- sag-7%— —. assert. tea-0%
b-fg; b=\2ro.W OU- Qs'bi 0y: 7:6 .Ci —- C nmex qu) 25-8 - 09m)
ob: -%%-81 Q (c) What percent of the variation observed in the response variable is explained by this linear a regression?
We r ». 0\Z.%3"Zs
Atoll: A’Zfb Question 10: A statistician calculated the least-squares regression of a response variable Y on an
explanatory variable X. The value of T2 was found to be exactly 1. The statistician then calculated
the residuals from the regression and plotted the residuals (on the vertical axis) versus the values
of X (on the horizontal axis). Give a description, in words and/or with an appropriate sketch, of
what the residual plot looked like. W (2. no erch r
' +56% Once; all on Aha, ("Willi—9:59am
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Read, \ x—oome; 0-} \z%\\:° Question 11: Let X be a variable following a normal distribution with a mean of 20 and a standard
deviation of 3. Deﬁne the variable Z as: $508 wndncd “E Z Z X — 20 N35 r N L I ‘ i
W '10“ 3 19 w '29; (a) What is the mean of Z? : O (b) What is the standard deviation of Z ? 1. \ Question 12: Brieﬂy describe Why it is important to utilize randomization when securing a sample
from a given population. Limit your answer to 4 sentences or less. » hie-“3% to maxim bloc-a
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