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Unformatted text preview: AEM 410
Fall 2005 Name Midterm Please circle the correct answer. 1.) 2.) A characteristic of nonparametric tests is that 0‘!” >
.> O (i9 they require assumptions about the population distribution
they evaluate hypotheses about the population distribution
they require numerical values for each element. none of the above In a oneway ANOVA with 3 groups, a rejection of the null hypothesis implies that the 3 population means are equal to each other. the 3 sample means are, equal to each other. each population mean differs signiﬁcantly from all other population
means. each sample mean differs signiﬁcantly from all other sample means.
some subset of population means differs from some other subset of
population means. some subset of sample means differs from some other subset of sample
means. 3.) Subject visibility
Test taker success
Interaction 1 1 1
Error 36 11,664.90
Total 9 4.) Psychologists have found that people are generally reluctant to transmit bad news
to their peers. This phenomenon has been termed the “MUM effect.” To
investigate the cause of the MUM effect, 40 undergraduates at Duke University
participated in an experiment. Each subject was asked to administer an IQ test to
another student and then provide the test taker with his or her percentile score.
Unknown to the subject, the test taker was a bogus student who was working with
the researchers. The experimenters manipulated two factors: subject visibility
and success of test taker, each at two levels. Subject visibility was either visible or not visible to the test taker. Success of the test taker was either visible or not
visible to the test taker. Success of the test taker was either top 20% or bottom
20%. Ten subjects were randomly assigned to each of the 2 x 2 = 4 experimental
conditions, then the time (in seconds) between the end of the test and the delivery
of the percentile score from the subject to the test taker was measured. (This
variable is called the latency to feedback.) The data were subjected to
appropriate analyses with the following results: Source df SS MS 1380.24 1380.24 4.26
1325.16 1325.16 4.09
3385.80 3385.80 10.45
324.00 FPR>F 0.043
0,050
0.002 3 17,755.20 In the context of this study, interpret the statement: “Subject visibility and test
taker success interact.” S a) The difference between the mean feedback time for visible and nonvisible
subjects depends on the success of the test taker.
b) The difference between the mean feedback time for test takers scoring in
the top 20% and bottom 20% depends on the visibility of the subject.
c) The relationship between feedback time and subject visibility depends on
the success of the test taker. ‘
All of the above are correct interpretations. The KruskalWallis test is analogous to the parametric procedure for analyzing
the data from a . ‘ , a.) correlation study b.) randomized complete block experimental design
completely randomized experimental design
paired comparison design 5.) An appliance manufacturer is interested in determining whether the brand of
laundry detergent used affects the average amount of dirt removed from standard
household laundry loads. An experiment is set up in which 10 laundry loads are
randomly assigned to each of four laundry detergents — Brands A, B, C, and D ( a
total of 40 loads in the experiment). The amount of dirt removed, y, (measured in
milligrams) for each load is recorded and subjected to an AN OVA analysis,
including a followup Tukey analysis. Which of the following inferences
concerning the Tukey results below is incorrect? Means 137 145 174 185
Brands C A '/ D B MD<MB b.) Mc<MD 0) MA < MB 0) MB > MC 6.) Suppose a company makes 5 different frozen dinners, and tests their ability to
attract customers. They test the frozen dinners in 14 different stores in order to
account for any extraneous sources of variation. The company records the
number of customers who purchase each product at each store. What assumptions
are necessary for the validity of the F statistic for comparing the response means
of the 5 frozen dinners? a.) The probability distributions of observations corresponding to all the
blocktreatment combinations are normal. The sampling distributions of
the variances of all blocktreatment combinations are normally distributed. . b.)‘ None. The Central Limit Theorem eliminates the need for any
assumptions c.) The means of the observations corresponding to all the blocktreatment
combinations are equal. The variances of all the probability distributions are equal.
The probability distributions of observations corresponding to all the blocktreatment combinations are normal. The variances of all the
probability distributions are equal. 7.) If a test for blocking in analysis of variance is signiﬁcant, it is likely that the test
for the differences between treatment means will be more sensitive, thus
the likelihood of the null hypothesis.  increasing/accepting
6’ increasing/rejecting
c.) decreasing/rejecting d.) decreasing/accepting '
e.) none of the above 8.) 9.) 10.) @ In a ChiSquare test, by combining cells we guard against having an inﬂated test
statistic that would have led us to Incorrectly reject the null hypothesis. b.) Incorrectly accept the null hypothesis. c.) Incorrectly reject the alternative hypothesis.
d.) none of the above. Which assumption concerning a multinomial test must be satisﬁed if your test
statistic is to have a chisquared distribution? The probability that the outcome of a single trial will fall into a cell must
remain the same from trial to trial b.) Each cell must have at least ﬁve observations 0.) Each cell must have no more than ﬁve observations (1.) The underlying distribution of the observations must be normal Many companies use wellknown celebrities as spokespersons in their TV
advertisements. A study was conducted to determine whether brand awareness of
female TV viewers and the gender of the spokesperson are independent. Each in a
sample of 300 female TV viewers was asked to identify a product advertised by a
celebrity spokesperson. The gender of the spokesperson and whether or not the
viewer could identify the product was recorded. The numbers in each category are
given below. Identiﬁed product 41 61
Could not
identify 109 89 Referring to the table above, which test would be used to properly analyze the
data in this experiment?
test for independence.
) test for difference between means.
c) AN OVA F test for main treatment effect.
(1) test for goodness of Please show all your work. 11.) (a) c 9
(u) 1 ’s (2» DH":F~"3O> 193"“; F3"3 23
3) T8. In order to understand what motivates students to enter a sales career, a
questionnaire was mailed to college students who indicated interest in going into
sales. The data below show the responses of 965 students. Each student listed the
most important factor that motivated him or her to consider a sales career. Number Saying This is
Factor » The Most Important Factor
Jo‘b itself 395 4 8‘ ‘7. 5
Pay 23 1 ~ 2 8' 9 , 5
Advancement & sense of achievement 231 3%"), 5
Other reasons 108 9],, 5 (Source: Adapted from S.Castleherry, "The Importance of Various Motivational
Factors to College Students Interested in Sales Positions," Journal of Personal Selling and Sales Management 10, no.2, (1‘990):65.) A marketing sales manager believes» that there is no difference among the
reSpondents' selection of the ﬁrst three factors and that the last factor (other
reasons) accounts for 10% of the students“ selection. Do the data support this
belief? Use a .10 signiﬁcance level. 0) f‘l ‘1 'lo
HM a} leasf om MP0 Mslaeot value
A = I Z(¢t' ’Cé32 . 2. .7
7C(1am. (395—arms)"
1‘393 57 1;”; :1 4.; (’03“95.5>l 92.5 v + t a Q
Fmbaloﬁu‘y does noi’ 23%] W @ a 59.45 4—11.89” u.<r2.+‘).3? =(é3.%§ G3 Ho 03’: A=./O (90 Th». dosh does inci sufforl’ W loehe, g, (D 12.) A college mathematics department has put together an exam for students who
have had calculus in high school. Those students who pass the test will be given
3 hours of college credit. For security purposes, the department Wishes to
develop and rotate three different versions or forms of the exams. A prime
consideration is to have an equivalent degree of difﬁcult for all tests. If 120
randomly assigned students now have taken the test versions with the results
given here, is it reasonable (at a = .10) to conclude that the objective of equivalent forms has been achieved? ,.
X 1 = 67.6)(2 = 65.8, 353 = 68.2, mm = 112 = 113 = 40, SS(E) = 6072.20 T. = 2404, T2 um, 73 = 273? (‘1)
33 (Ta) = 1],}, 240%, 21,512+ ;¥2Y’ﬂ —— “6’sz
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02C {Zulua/envt perms Aas W chem/cued], 13.) Each year the personnel department in a large corporation assesses the ‘
performance of all of its employees. Each employee is rated for various aspect
of his or her job on a 7point scale where 1 = very unsatisfactory and 7 = very
satisfactory. The president of the Company believes that the median assessment
scores this year are 10wer than last year's. To examine the validity of this belief
she draws a random sample of six employees' scores from last year and another
six employees' scores this year. Do the data listed below allow the president to
conclude at the 5% significance level that her belief is correct? (10)
Employee Ratings Scores
Last Year This Year
5 £9) ‘ 5 (9)
6 ((5,?) 5 ((93
4 o 3 3
5 m 3 (a) @ mm“
5 (9) 4 (56)
3 (3) 2 (:3
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’Dt‘l'h/eeh Ho’s yeaw and last year. ’ Her 'be/Iér‘ 15 nol— Qumc/ 7‘0 $5 CorrecLL, CD 14.) A national automotive repair service is interested in studying the effect of
automobile manufacturer and vehicle model on the time required to complete a
brake replacement job involving all four wheels. The study was limited to the
"Big Three" U.S. manufacturers (Ford, GM, and DaimlerChrysler) and to two
models (passenger cars and sport utility vehicles). Five vehicles of each model , and manufacturer were tested, and the time required to complete the brake job
was recorded. The summary statistics are given below. Manu acturer
COman A Coman B Coman C 32  60.2 i = 65.4 i  76.8
Vehicle Model _ 101
SE  97.2 if  92.6 x ' a.) Plot the mean brake change time for each manufacturer for each of the
model types (i.e. put the Companies on the horizontal axis). Looking at
the graph, what conclusions do you reach about the interaction between
model type and manufacturer? Thine. C1085 “0+ af‘Pear 7L0 be an IDWQC‘AM
' bel’ween 4“ Cars and W companies.
3'0 hQVe\ 0" “\SlNI—V mean 41% a b.) (H7 (5) Complete the following ANOVA Table . / Source SS . (if (/7 1 Ms t F7 673.8 3 01¢ 0 224.07 _ ,9. [a >, 05 Company
Model 379% /58‘
11204.8 39 5 i , Error Total (£6’ééy 7‘5“ 00/1“; /45£/’Q  '5 é5/2,/3 Based on the sample data, is there interaction between manufacturer and model type? Test using a significance level equal to 0.05. Note: just use
the information from above and list your hypothesis and the justiﬁcation for your conclusion (you do NOT need to write out the six steps). ALSO 
Discuss the implications of this result as it relates to this study. 77mm )5 nof s/jn;£m¥ m ¢erac+;ovt
mama p>,05,@ /nr¢,/0/IC&L7‘70'775 ~ >6“ CCU/l aha/>125 54%
mcun e££§c+5 C Com/Games 4' Mode/s) 6) Sep anuLe {<0 I] (1.) Based on the sample data, can you conclude that a difference exists in
mean brake repair times for passenger cars versus SUVs? What
conclusions should the automobile repair company make regarding the
brake repair times for the three manufacturers? (Note: you do not need to
list the six steps each time, simply justify your conclusion). If appropriate,
use the Tukey procedure for multiple comparisons with an experiment~
wise signiﬁcance level of 0.05 (for either or both tests). Discuss your results. If the comparisons are not appropriate, explain why not. There, '6 {10+ 0L sljmgm} dlpfgranCL
@ he’lween 44¢ CWmleS (,0 >195), mfg; [‘5 a Sljnllqau’l‘ll @m past cars anal Sal/s 90(1),) Cmara Cars qt Jug; 16) (9) In part of a statistical analysis by Kauﬁnan and Wolf, 2002, they described
examining the preferences and anxieties of men and women with respect to
attending job interviews in hotel rooms. The table gives additional data from this
study. A random sample of 302 students (95 men and 207 women) was asked
whether they would be uncomfortable about interviewing in a hotel room. The
responses (row percentages) are shown in the table. _ .... .................. .‘
Men ....... .......................... ........... ..
........... a.) Do these data provide sufﬁcient evidence to conclude that anxiety over hotel room interviewing is related to the interviewee’s sex Test using
0t =.05. I.) “0: nnXlC‘l’y ;5 07C W Inwruzewee '5 H4: V ’5 mi“ N 1&3
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What is the approximate p value for your test statistic? '0/4‘10<‘0:95i b.) say 9 Construct a plot of the proportions who are uncomfortable or not using sex as
the baseline to help interpret the result of the test in part (a).Include a sentence
evaluating your graph. l4 EXTRA CREDIT A large corporation sends many of its ﬁrstlevel managers to an offsite
supervisory skills course. F our different management development centers offer
this course, and the corporation wants to determine whether they differ in the
quality of training provitied. A sample of 20 employees, who attended these programs is chosen and the employees ranked in terms of supervisory skills. The
results follow. L ‘ Suerviso 1 Skills Rank Note that the top—ranked supervisor attended course 2 and the lowest ranked
supervisor attended course 4. Use (1 = .05 and test to see whether there is a
signiﬁcant difference between the median rankings of the training provided by the
four programs. /.7 Ho "ﬂag/{lav~ 5/45 “H4 Alafaé' leasi‘ m m Méjw/ @ 2.) pt: ,05 Z
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