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Unformatted text preview: Section 24 Name Red Id STAT 119 EXAM ONE
February 28, 2008
Form C You have 75 minutes to complete this exam. Mark your answers neatly on the exam and be sure
to Show all your work. Please round your answers to four dig its after the decimal. when possible.
Make sure to put your final answers neatly within the answer boxes {when provided). Please
CIRCLE the correct answer and use CAI’ITAL LETTERS in the space provided for the
multiple Choice. BE CAREFULE GOOD LUCK! Page 1 Total
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0' Multi 1e choice nestions are worth 3 oints each
1. A market researcher randomly seiected two Itaiian restaurants from all Italian restaurants in Girl
Town and interviewed all customers in each restaurant. What sampiing method was used?
A. Convenience Sample
B. Simple Random Sampie
C. Stratified Sampie @ Cluster Sample Answer: I 2. What could go wrong with the particular sample selected in the previous problem?
A. The sampie size may be too large, which makes reading the data difﬁcuit.
B. The customers selected from a restaurant may create an unbiased sampie.
{if} The chosen restaurants may not accurately represent all Italian restaurants in old Town.
D. The restaurants are selected at random; the data is therefore reiatively unreiiable. as;
Answer: 3. On a given day. the NYSE opening price per share for the 100 largest US. corporations has a
mean of S385 and a median of $92. We can conclude:
{g} The distribution of the price per share is skewed to the right.
B. The distribution of the price per share is symmetric.
C. The distribution of the price per share is skewed to the left.
I). There must he a mistake: there is too iarge of a discrepancy between the mean and
median. Answer: I 4. An IQ test follows a normal distribution with a mean of 100 and standard deviation of 21.
84 percent of IQ scores wiii fail above which value? A. :42 B. 58 C, 84 o. 121 © 79 Answer: u 5. iohn is enrolied in a caicuius course and has received his score on the midterm exam. His score
on the midterm was .114, and the professor has indicated that his zscore was 0.78. What is the
best interpretation of the meaning of this z—score? A. Seventyeight percent of ali students taking the exam had scores above his. His score was 0.78 standard deviations above the mean of all scores.
. His score was 0.78 IQR above the median of all scores.
. He got 78% of the prohiems on the test correct.
. Seventy—eight percent of ail students taking the exam had scores below his. Answer: Total: (15) 6. The histogram below was generated by a Stat 119 class. It shows the heights of a sample of
freshman students. 3
n
u
n.
u
t
n
n
. It was determined that the outlier or: the left resulted from a height being incorrectly entered. This
incorrect data point was removed from the data and a new histogram was made and ali new
statistics were calculated. Which of the foliowing statements is/are true? When the incorrect data
point is removed: A. The mean and standard deviation wilt both be smaller @ The mean will be larger, but the standard deviation will be smaller C. The mean will be srnalier, but the standard deviation will be iarger D. The mean and standard deviation wiEi both be larger E. None of the above Answer: 7. A State University groep is interested in whether voters would support lowering the legal
drinking age to 18. They have chapters on each of California‘s major universities. Each of these
chapters randomly selected 25 students and asked whether they approve of lowering the drinking
age. The most signiﬁcant bias introduced here is: A. Convenience Sampling
B. Response Bias C. Non Response Bias
£3 Undercoverage Answer: 8. In the context of regression analysis, which of the foliowing statements are aiways true?
i. Outliers wiil affect the value of coefficient of determination. ‘5?
11. When the sum of the residuais is greater than zero, the model is nonlinear. g
III. A point has high leverage if including it results in a different regression model. ii;
I only
II only
III only
I and ii only
I, II, and HI Answer: 5%
Total: (9) muons ix) 9. A researcher uses a regression equation to predict home heating bills (dollar cost), based on borne
size (square feet). The correlation between predicted bills and home size is 0.70. What is the
correct interpretation of this finding? A. 70% of the variability in home heating bilis can be explained by home size. : 49% of the variability in home heating bilis can be explained by home size. . For each added square foot of home size, heating bills increased by 70 cents.
D. For each added square foot of home size, heating bills increased by 49 cents.
E. None of the above. Answer: it). Which of the foilowing is always false regarding residual plots?
A. A negative residual indicates an overpredictiort.
B. A srnail residual indicates a good prediction at that particular data point.
C. Patterns in a residual plot as a whole indicate poor predictive power.
g} Uneven variation in a residual plot indicates strong predictive power.
E. A large residual indicates an overprediction. Answer: 11. The boxplots beiow summarize the distributions of SAT verbal and math scores among students
at an upstate New York high school: Boxplot of Math, Verbai Math Verbal  1 , t . y
330 400 565 500 700 805
Data Whi h of the following statements is false?
{j The verbal scores are roughiy symmetric, while the math scores are skewed to the right.
8. The range of the math scores equais the range of the verbal scores.
C. The highest math score equals the median verbal score.
D. The interquartile range for the math scores is smailer than the interquartile range for the
verbal scores. Answer: Totai: J9} 12. J aei; scored 82 on a test in which mean was 76 with standard deviation of 7. Jill scored 85 on the
test in which mean was 78 with standard deviation of 8. If the scores are normally distributed,
who scored better on their test relative to the rest of their class? A. Cannot be determined, because they are in different classes
@ Jill, since her zwseore was higher C. Jack, since his z—score was higher D. J ask, since the standard deviation was smaiier E. .Tili. since the mean was higher Answer: 13. in generai, which of the following statements is FALSE?
A. The sample mean is more sensitive to extreme values than the median.
Q The IQR is more sensitive to extreme values than the standard deviation.
C. The sampie standard deviation is a measure of spread around the sample mean.
D. If a distribution is symmetric, then the mean will be eq‘aai to the median. Answer: 14. Below you will ﬁnd a histogram of the average wind speed in miles/hour of 43 days in Hawaii. Wequency Wind steed hich of the following statements regarding the distribution above is INCORRECT? The median wind speed is in the (45—50) mph intervai and the third quartile is within the (50— 55) mph intervai.
B. The median wind speed is in the (45—50) mph interval and the first quartile is within the (35
40) mph interval.
The distribution of wind speeds has a negative skew.
Because of the gap in the distribution, the one day in the (05) mph interval is likely to be an
outlier. Answer: .UO Totai: (9) 15. (4 points) The mean value of iand and buildings per acre from a sample of Farms is normally
distributed with a mean value of $i500 and a standard deviation of $200. Use the Empirical rule to estimate the percent of farms whose land and building vaiues per acre are between Sl 100 and
$2100. at; as get?“ :%§X§s§
2.7. as s 7 get tea? is Use the foilowing information to answer probiems 1618 g20 points}: A physicalfitness association is including the mile run in its secondarymschooi ﬁtness test for students.
The time for this event is normally distributed with a mean of 470 seconds and a standard deviation of 45
seconds. 16‘ (7 points) What proportion of secondary—school students have a mile run time that is slower than 9 minutes (540 seconds)? 3 A? .7; m Answer: a g t: g ﬁ 1% ' r. E7. (7 points) What proportion of secondarysehool students have a mile run time between 4t0 and  ,, , m, ,.._ _ B
u r if: tee
es antagogg ée tinge”? n; r%t§s%%m a ﬁﬁttg
Answer: fl: t 18. (6 points) If the association wants to designate the fastest 7.5% of secondary school students as
“exceilent”, what time should the association set for this criterion? a :1 a iteettﬁiie site
i;— ganglia Answer: Total: 424} E9. (7 points) The board of examiners that administers the reai estate brokers’ examination in a
certain state found that the scores were normain distributed with a standard deviation of 69. If the
passing score is 430, and only the top 27% pass the examination, what is the mean score on the
reai estate brokers’ examination? S is f :: isgﬂ j: 2:. 3 see; e “ii Answer: Use the foilowing to answer 'Qroiﬁems 2623 523 gointst: The houriy earnings (in dollars) of a sample of 15 restaurant workers are shown beiow:
9.1 10.7 1£.1 1i.4 11.7 “.8 i2.2 12.2 12.5 12.6 12.6 12.7 12.7 13.1 13.4 a ﬁg iéziiéﬁﬁ r E 20. (6 points) Construct a spiit—stem plot for the data Wits: $3; give iivei 2?... (6 points) Is the hoeriy wage of $9.1 an outiiet? CEeariy show aIi work. Ease: ﬁnesse m 3.9% y E
@iw :3 its is: iiaismi.%t:i3§ rs‘iieﬁg tit iii “"3?
it s: e— s see. 3; tea; m sites“; see 23. (6 points) Caiculate the standard deviation and {QR for the distribution. Which is the best choice
of spread for this distribution? Justify your Choice in one sentence: Standard deviation i e igg E g" IQR i 3 % Choice of Spread Justification of choieewwm at; Total: (30) Use the following to answer problems 2427 119 points}: A random sample of 1027 adults was classiﬁed by party affiliation and whether they would supposz a
mandatory Health care plan. F 1 support Oppose i Unsure 1 Total 1 Democrat 256 163 t 22 l 441 l
3 Republican 1 235 222 i 5 l 462 t
1 Independent  60 40 2;: 1 i124 l
\ Totai t 55; 425 1 SE  1027 1 Answer 26$. (4 points) What percent of ali aduits were Republican and support a mandatory heaith care plan? iia ‘M «@233 25. (4 points) Of the Democrat adults, what proportion opposes the mandatory health care plan? % %at w
M agaie 26. {6 points) Complete the tabie below to show the conditional distribution of mandatory health plan
opinion, conditioned on party afﬁiiation. Show your work for full credit. Support Oppose i Unsure  Democrat aﬁi‘ggﬁg Eﬂ:*3é£€§e I
set as»: ‘ Wei Republican gigg’gﬁig? ﬂga5§§§§§ﬂ iiis$i§§§yl
aaa as; E gee?” is i g ' M e"; Independent EEK» :3” ii” :33 3i 9*" ” 5 we we 1 ea 27. (5 points) Do you think that party affiliation is independent of support of a mandatory heaith care plan? Expiain. jwﬁaiw (19) C Use the followin information to answer roblems 2832 25 oints :
H'orricanes develop Eow pressure at their centers. A sample of 163 hurricanes (with central pressure
ranging from 910 to 1000 mb) was studied to investigate the relationship between central pressure (rub)
and maximum wind. speed (knots). The data was analyzed to produce the results below: Regression equation: Max wind speed = 955.2? m 0.897Ccmral Pressure R«squared m 77.24% 28. (6 points) What is the correlation between the central pressure and maximum wind speed? Use
this value to assess the strength of the linear association. {it 2%: Fermi—g is???" 13% 17W“ t g ,, Interpretation fiﬂﬁﬁlfit’ﬁ 293%}; Correlation coefﬁcient: §5i§§ saggy ﬁfié rotates 29. (6 points) identify and interpret the slope for the above equation. Slope: as v ‘ Interpretation ﬁtﬁﬁg iﬁﬁéﬁé‘t’; g? i W Mg ﬁresit’ttaefi testith 3 30. (6 points) Hurricane Katrina had a central pressure of 920 mb. if the residual for this model
value is «18, what is the true maximum wind speed for this centrai pressure? sergeant Weaatami :2: tsetse gesiétenl :3 if“?
sag,» F t? .s issue’s as yﬁiﬁee’setgx lists? Answer: a 3i. (3 points) A hurricane has a calculated residual that is negative. Which of the following is a correct statement?
A. Since the residual is negative the prediction must be accurate.
B. The residual valne indicates that the prediction is too low. @ The residual value indicates that the prediction is too high
. We cannot determine whether the prediction is too low or too high from a residual value. 49m, Answer: 32. (4 points) Wouid it be appropriate to use the above model to predict maximum wind speed for a
hurricane with central pressure lit)0mh? Expiai % y \E
i l i " iﬁsgﬁﬁs an: ass 32% sets Total: (25} ...
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