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Unformatted text preview: 11.2 Comparing Two Means (at Fill in the values in this sununarv table: Group treannenr n x s
1 lDX ? ? ?
2 Untreated ? ? ? (b) What degrees of freedoln would you use in the conservative two—sample t proce
dures to compare the two treatments? 11.52 TREATING SCRAPIE,  Exercise 115] contains the results ofa study to determine
whether IDX is an effective treatment of scrapie. {a} Is there good evidence that hamsters treated with IDX live longer on the average? {tr} Give a 95% confidence interval for the mean amount by which IDX prolongs life. 11.53 TEACHING READING An educator believes that new reacting activities in the classroom
will help elementary school pupils improve their reading ability. She an‘angcs for a third
grade class of 21 students to follow these activities for an 8—week period. A control classroom
of 23 third graders follows the same curriculum without the activities. At the end of the 3
weeks, all students are given the Degree of Reading Power (DRP) test which measures the
aspects of reading ability that the treatment is designed to improve. Here are. the (lat‘ :22 Treatment Control 24 43 58 T] 43 42 4% 55 26 62
4‘) 6] 44 67 4‘) 37 33 41 19 54
5% 56 59 32 62 20 85 46 10 17
'34 5? 33 46 43 60 53 42 3? 42
'3? 55 28 48 {a} Examine the data with a graph. Are there strong outliers or skewness that could
prevent use of the t procedures? (b) Is there good evidence that the new activities improve the mean DRP score? Carry
out a test and report your conclusions. (c: Although this study is an experiment, its design is not ideal because it had to be done
in a school without disrupting classes. W'hat aspect of good experimental design is missing? 11.54 WEIGHT LOSS PROGRAM In a study of the effectiveness ofa weight loss program, 47
subjects who were at least 20% overweight took part in the program for 10 weeks.
Private weighings determined each subject’s weight at the beginning of the program
and 6 months after the program’s end. rf' he matched pairs t test was used to assess the
significance of the average weight loss. The paper reporting the study said, “The sub—
jects lost a signiﬁcant amount ofweight over time, H46) 2 4.68, f) < Hi.” It is com
mon to report the results of statistical] tests in this abbreviated style.23 {a} “7hr was the matched pairs 1‘. test appropriate? (bl Explain to someone who knows no statistics but is interested in weight—loss pro
grams what the practical conclusion is. 659 571} Chapter 11 Inference for Distributions (c) The paper follows the tradition of reporting significance only at ﬁxed levels such
as a : 0.01. In fact, the results are more significant than “p < .01” suggests. Use Table
C to say more about the P—valuc of the t test. 11.55 COMPARING TWO DRUGS Makers of generic drugs must show that they do not differ
signiﬁcantly from the “reference” drug that they imitate. One aspect in which drugs might
differ is their extent of absorption in the blood. Table 1 1.6 gives data taken from 20 heal thy
nonsmoking male subjects for one pair of drugs. This is a matched pairs design. Subjects
1 to 10 received the generic drug first, and Subjects 11 to 20 received the reference drug
First. In all cases, a washout period separated the [we drugs so that the ﬁrst had disappeared
from the blood before the subject took the second The subject numbers in the table were
assigned at random to decide the order of the drugs for each subject. (a) Do a data analysis of the differences between the absorption measures for the
generic and reference drugs. Is there any reason not to apply t procedures? (b) Give a 90% conﬁdence interval for the mean difference in gains between treatment
and control. TABLE 11.3 Absorption extent for two versions of a drug Refererte Generic Reference Generic Sumen dmg one Bowed dmg dmg
15 4108 1755 4 234e 2738
3 2526 1138 16 186" 2302
9 2729 1613 ' 6 1022 1284
13 3852 2254 I 10 2256 3052
12 1833 1310 j 5 938 1287
8 2463 2120 7 1339 1930
18 2059 1851 14 1262 1964
20 1709 1878 = 11 1438 2.549
17 1829 1682 1 17.35 .3340
2 2594 2613 t 19 1020 3050 Source: Data from Lianng Yuli, “A biopharmaceutieal example for
undergraduate students," unpublished manuscript. 11.55 EUAEHING AND SAT SCORES Coaching companies claim that their courses can raise the
SAT scores of high school students. Of course, students who retake the SAT without pay—
ing for coaching generally raise their scores. A random sample ofstudcnts who l’Ole' the
SA’ 1 ' twice found 427 who were coached and 2,733 who were uncoached.24 Starting with
their Verbal scores on the ﬁrst and second tries, we have these summary statistics: Trgl 1th Gain
Mean Std.dev. Mean Std.dev. Mean Stddev. Coached 500 92
Uncoached 506 101 527 101 21 52 11.2 Comparinng Means Let’s ﬁrst ask if students who are coached increased their scores significantly. {at You cordd use the information given to carry out either a twosample t test corn—
paring Try 1 with Try 2 for coached students or a matched pairs t test using Gain.
Which is the correct test? Why? {1)} Carry out the proper test. What do you conclude? {'c) Give a 99% confidence interval for the mean gain of all students who are coached. 11. 5? EUAEHING AND SAT SCORES,  What we really want to know is whether coached stu—
dents improve more than uncoached students, and whether any advantage is large
enough to be worth paying for. Use the information in the previous problem to answer these questions. {a} Is there good evidence that coached students gained more on the average than
uncoaehed students? {b} How much more do coached students gain on the average? Give a 99% conﬁ
dence interval. {U} Based on your work, what is your opinion: do you think coaching courses are
worth paying for? 11.58 COACHING AND SAT SCORES: CRITIQUE The data yOu used in the previous two exer—
cises came from a random sample of students who took the SAT twice. rt'he response
rate was 63%, which is pretty good for nongovernment surveys, so let’s accept that the
respondents do represent all students who took the exam twice. Nonetheless, we can’t
be sure that coaching actually caused the coached students to gain more than the
uucoach ed students. Explain brieﬂy but clearly why this is so. 11.59 STU DENTS' SELZLEDNEEPT Here is SAS output for a study of the sclf~concept of seventh—
grade students. The variable SC is the score on the Pierswl—Iarris Self Concept Scale.
The analysis was done to see if male and female students differ in mean self—concept
SCOICLZs TTEST PROCEDURE Variable: SC SEX N Mean Std Dev Std Error
F 31 55.5..612903 12.69611743 2.28029001
M 47 57.92.4'89362 12.26488410 1.78901722
Variances T DF Prob>  T ]
Uneqaal —0.8276 628 0.4110
Equal —0.8336 76.0 0.4071 Write a sentence or two Summarizing the comparison of females and males, as if you
were preparing a report for publication. ﬁ?2 Chapter 11 Inference for Distributions The remaining exercises concern the power ofthe twosample t test, an optioncii topic.
ifyou have read Section 10.4 and the discussion of the power of the one—sampie t test on
pages 639—640, Exercise 11.61 guides you in ﬁnding the power ofthe two—sample at. 11.60 111 Example 11.10 (page 650), a small study of black men suggested that a calcium
supplement can reduce blood pressure. Now we are planning a larger clinical trial of this
effect. We plan to use 100 subjects in each of the two groups. Are these sample sizes large
enough to make it very likely that the study will give strong evidence (a : 0.01) of the
effect of calcium it in fact calcium lowers blood pressure by 5 millimeters more than a
placebo? rlb answer this question, we will compute the power of the tuD—smnple t test of against the speciﬁc alternative M1 — 1L3 : 5. Based 011 the pilot study reported in
Example 1 1.10, we take 8, the larger of the two obscured s—values, as a rough estimate
of both the population {7’5 and future sample 3’s. (a) that is the approximate value of the a : 0,01 critical value if“ for the two—sample
1. statistic when :11 : u2 : 100? (1)) Step 1: Write the mile for rejecting 1'1“ in terms of f1 — 352. The test rejects HLJ when Take both 31 and 32 to be 8, and ul and rig to be 100. bind the number 0 such that the
test rejects H‘J when f1 — E2 2 c. to) Step 2: The power is the probability of rejecting 11[) when the altemative is true.
Su ose that p. — u, = 5 and that both or and 0‘1 are 8. The owcr we seek is the )rob— PP 1 _ 1 L P l
ability that E1 — E2 2 c under these assumptions Ca1culate the power. (d) Describe a Type 1 and a Type I] error in this experiment. Much is more serious? 11.61 A bank asks you to compare two ways to increase the use of its credit cards. 1’1 a n
A would offer customers a cash—back rebate based on their total amount charged. Plan
B would reduce the interest rate charged on card balances. 'l 'he response variable is the
total amount a customer charges during the test period. You decide to offer each cat—Plan
A and Plan B to a separate SRS of the bank’s credit card customers. In the past, the
mean amount charged in a six—month period has been about $1100, with a standard
deviation of $400. Will a twosamplc t test based on SRSs of 350 customers in each
group detect a difference ot$100 in the mean amounts charged under the two plans? (a) State H“ and H”, and write the formula for the test statistic. (b) Give the CE = 0.03 critica1 value For the test when n] : :11 = 3'50. (c) Calculate the power of the test with or 0.05, using $400 as a rough cstiu'iatc of
all standard deviations. td] Describe a '1"vpe 1 error and a Type 11 error in this setting. Which is of more con
cern to the bank? .F 11.2 Comparing Two Means 573 CHAPTER REVIEW This chapter presents t tests and conﬁdence intervals for inference about the
mean of a single population and for comparing the means of two populations.
The oneisample t procedures do inference about one mean and the two—sample
t procedures compare two means Matched pairs studies use one—sample proce—
dures because you ﬁrst create a single sample by taking the differences in the
responses within each pair. 'lhese t procedures are among the most common
methods of statistical inference. 'Ihe ﬁgure below helps you decide when to use
them. Before you use any inference method, think about the design of the study
and examine the data for outliers and other problems. The t Procedures for Means STUDY DESIGN?
One Sample Matched Fairo, Two Sample DATA ANALYSiS: CAN WE U5E t2?
Strong Skewnaos? Outliers)? Small Sample? CHOOSE t PROCEDURE The t procedures require that the data be random samples and that the dis
tribution of the population or populations be nornlai. One reason for the wide
use of t procedures is that they are not very strongly affected by lack of nor—
mality. If you can’t regard your data as a random sample, however, the results
of inference may be oflittle value. Chapter It] concentrated on the reasoning of conﬁdence intervals and
tests. Understanding the reasoning is essential for wise use of the t and other
inference methods. The discussion in this chapter paid more attention to prac
tical aspects of using the methods. We saw that there are several versions of the
tworsainple t, for example. Which one you use depends largely on whether or
not you use statistical software. Before you use any inference method, think
abOut the design of the study and examine the data for outliers and other prob—
lems The chapter exercises are important in this and later chapters. You must
now recognize probiem settings and decide which of the methods presented
in the chapter fits In this chapter, you must recognize oncesample studies,
matched pairs studies, and two~sarnplc studies. Here are the most important
skills you should have after reading this chapter. A. RECOGNITION 1. Recognize when a problem requires inference about a mean or comparing
two means. Dﬁoign? T551: or" Confidence Intervai? g l
PRACTICAL CONCLUSION? 574 Chapter 11 CHAPTER 11 REVIEW EXERCISES Inference for Distributions 2. Recognize from the design of a study whether onesample, matched pairs,
or two—sample procedures are needed. B. ONESAMPLE t PROCEDURES 1. Use the t procedure to obtain a confidence interval at a stated level of con—
ﬁdence for the mean [.L of a population. 2. Carry out a t test for the hypothesis that a population mean ,u has a speci—
fied value against either a onesided or a two—sided alternative. Use Table C 03‘
t critical values to approximate the P—value or carry out a ﬁxed or test. 3. Recognize when the t procedures are appropriate in practice, in particular
that they are quite robust against lack of normality but are influenced by outliers. 4. Also recognize when the design of the studyP outliers, or a small sample
from a skewed distribution make the t procedures risky. 5. Recognize matched pairs data and use the t procedures to obtain confi—
dence intervals and to perform tests of significance for such data. C. TWOSAM PLE t PROCEDURES 1. Give a confidence interval for the difference between two means. Use the
two—sample 1‘ statistic with conservative degrees of freedom if you do not have
statistical software. Use the "Fl83,89 or software if you have it. A 2. Test the hypothesis that two populations have equal means against either a
onesided or a twosided alternative. Use the twousample t test with conserva
tive degrees of freedom if you do not have statistical software. Use the TI83i’89
or software if you have it. 3. Recognize when the two—sample tprocedures are appropriate in practice. 11.52 EXPENSWE ADS Consumers who think a product’s advertising is expensive often
also think the product must be of high quality. Can other information undermine this
effect? To ﬁnd out, marketing researchers did an experiment. The subjects were 90
women from the clerical and administrative staff of a large organization. All subjects
read an ad dlat described a ﬁctional line of food products called “Five Chefs.” The ad
also described the major TV commercials that would soon be shown, an unusual
expense for this type of product, The 45 women in the control group read nothing
else. The 45 in the “undermine group” also read a news story headlined “No link
between Advertising Spending and New Product Quality." All the subjects then rated the quality of Five Chefs products on a seven—point
scale. The study report ._said, “Thc mean quality ratings were signiﬁcantly lower in the
undermine treatment (Xﬂl = 4.56) than in the control treatment (XC = 5.05; t = 2.64,
p < .01).”26 (a) ls the matched pairs t test or the twosample t test the right test in this setting?
“div? (1)) W’ hat degrees of Freedom would you use for the t statistic you chose in (a)? (e) The distribution of individual responses is not normal, because there is only a
sevenpoint scale. Why is it nonetheless proper to use a t test? 11.53 SHARKS Great white sharks are hig and hungry. Here are the lengths in feet of44
great whilemx 18.7 12.3 18.6 16.4 15.7 18.3 14.6 15,8 14.9 17,6 12.1
16.4 16.7 17.8 16.2 12,6 17.8 13.8 12.2 15.2 14.7 12.4
13.2 15.8 14.3 16.6 9.4 18.2 13.2 13.6 15.3 16.1 13.5
19.1 16.2 22.8 16.8 13.6 13.2 15.7 19.7 18.7 13,2 16.8 {3) Examine these data for shape, center, spread, and outliers. 'I‘he distribution is rea—
sonably normal except for one outlier in each direction. Because these are not extreme
and preserve the symmetry of the distribution, use of the t procedures is safe with 44
observations. (b) Give a 95% confidence interval for the mean length of great white sharks. Based
on this interval, is there signiﬁcant evidence at the 5% level to reject the claim “Great
white sharks average 20 feet in length"? (c) it isn’t clear exactly what parameter p. you estimated in What information do
you need to say what ,u. is? 11.54 INDEPENDENT SAMPLES VERSUS PAIRED SAMPLES Deciding whether to perform a
matched pairs t test or a twosample t test can be tricky.28 Your decision should be based on the design that produced the data. Which procedure would you choose in
each of the following Situations? (a) To compare the average weight gain of pigs fed two different rations, nine pairs of
pigs were used. The pigs in each pair were littemiates. (b) To test the effects ofa new fertilizer, 100 plots are treated with the new fertilizer,
and 100 plots are treated with another fertilizer. (c) A sample of college teachers is taken. We wish to compare the average salaries of
male and female teachers. (d) A new fertilizer is tested on 100 plots. Each plot is divided in half. Fertilizer A is
applied to one half and B to the other. to) Consumers Union wants to compare two types of calculators. They get 100 vol
unteers and ask them to carry out a series of 50 routine calculations (such as figuring
discounts, sales tax, totaling 3 bill, etc.). Each calculation is done on each type of cal—
culator, and the time required for each calculation is recorded. 11.55 KIEKINE A HELIUMEILLED FDDTBAll On a calm, clear Saturday in 1993, the Auburn
'l‘igers were faced with fourth down deep in their own territory. "1111 eir opposition, the
Mississippi State Bulldogs, looked for good field position following a punt. The foot—
ball was snapped, kicked, and eyed in disbelief as it sailed an estimated 71 yards Chapter Review 575 675 Chapter 11 Inference for Distributions through the air. Shocked, the Mississippi State coaches cried foul and the football was
immediately seized by the officials. The football was later tested to see ifit had been
filled with helium, as many thought that this might explain its unusually long flight.
No helium was found in that football, but the possible benefits of filling a football with
gas lighter than air would be kicked around both science and sports communities in
the weeks to come. Many devised their own experiments to see if helium—filled balls
traveled farther than footballs fi1led with air. The Columbus Dispatch conducted one such study. "two identical footballs, one
air—ﬁlled and one helium—tilled, were used outdoors on a windless day at Ohio State
Universith athletic complex. The kicker was a novice punter and was not informed
which football contained the helium. Each football was kicked 39 times and the two
footballs were alternated with each kick. Table 11.7 provides the data from this exper—
uncut. TABLE Distance traveled (in yards) by two kicked footballs, one filled with helium and one ﬁlled with air Toal aw Hehum i tea as HeHum ] 1661 Ah‘ Heﬁum j 16a as HeHum
1 25 25 5 11 25 12 21 31 31 5 31 22 26
2 23 16 i 12 19 28 1 22 27 34 F 32 26 32
3 18 25 g 13 27 28 j 23 22 39 E 33 28 30
4 16 14 § 14 25 31 24 29 32 g 34 32 29
5 35 23 i 15 3 22 25 28 14 ; 35 28 30
6 15 29 t 16 26 29 26 29 28 j 36 25 29
3 26 25 i 17 20 23 1 27 22 30 i 37 31 29
8 24 26 E 18 22 26 f 28 31 27 38 28 3o
9 24 22 i 19 33 35 a 29 25 33 = 39 28 26 10 28 26 g 20 29 24 f 30 20 11 Source: Data from the EESEF‘. story “Kicking a lIcliumll‘illed Football.” Based on the summary statistics, the researcher concluded that there is “not much dif—
ference” in the results for the two footballs, {a} Perform an appropriate statistical test of this statement. (b) Conduct your test from (a) with any outliers in the data set removed. Compare the
two results. (c) 'I'he researcher also stated: “The kicker changed footballs on each kick, guaran
leeing that his leg would play no favorites if he tired. However, it appears he improved
with practice.” Perform an appropriate statistical analysis to address this claim. 11.55 LEARNING TD SGWE A MAZE Table 11.2 (page 629) contains the times required to complete a maze for 21 subjects wearing scented and unscented masles. Example 1 1‘1
used the matched pairs t test to show that the scent makes no signiﬁcant difference in
the time. Now we ask whether the re is a learning effect, so that subjects complete the
maze faster on their second trial. All of the oddnumbered subjects in rFable 11.2 first
worked the maze wearing the unscented mask. E1‘e11—nun‘1bered subjects wore the
scented mask first. 'I 'he numbers were assigned at randonL {a} we will compare the unscented times for “unscented first” subjects with the
unscented times for the “scented ﬁrst” subjects. Explain why this comparison requires
two—sample procedures. (b]I We suspect that on the average subjects are slower when the unscented time is
their first trial. Make a back—to—back sternplot of unscented times for “scented ﬁrst” and
“unscented first” subjects. Find the mean unscented times for these two groups. Do
the data appear to support our suspicion? Do the data have features that prevent use of
the t procedures? {c} Do the data give statistically signiﬁcant support to our suspicion? State hypothe~
ses, carry out a test, and report your conclusion. 11.57 EDMPARING WELFARE PROGRAMS A major study of alternative welfare programs
randomly assigned women on welfare to one of two programs, called “MN” and
“Options.” WIN was the existing program. The new Options program gave more
incentives to work. An important question was how Inuch more {on the average)
women in Options eamed than those in WIN. Here is Minitab output for earnings in
dollars over a 3—year period?” TWOSAMPLE '1‘ FOR ‘OPT’ VS ‘WIN’
N MEAN STDEV SE MEAN
OPT 1362 7638 289 7.8309
WIN 1395 6595 247 6.6132
95 PCT C: FOR MU OPT — MU WIN: (1022.90, 1063.10) (a) Give a 99% conﬁdence interval for the amount by which the mean earnings of
Options participants exceeded the mean earnings oleN subjects (Minitab will give
a 99% conﬁdence interval if you instruct it to do so. Here we have only the basic out
put, which includes the 95% confidence interval.) (b) The distribution of incomes is strongly skewed to the right but includes no
extreme outliers because all the subjects were on welfare. What fact about these data
allows us to use t procedures despite the strong skewness? 11.68 EACH DAY [AM GETTING BETFER IN MMH A “subliminal” message is below our thresh
old ot awareness but may nonetheless influence us. Can subliminal messages help stue
dents learn math? A group of students who had failed the mathematics part of the City
University of New York Skills Assessment Test agreed to participate in a study to find out. All received a daily subliminal message, Flashed on a screen too rapidly to be con—
sciously read. The treatment group of 10 students (chosen at random) was exposed to
Hliiacll day I am getting better in math.” The control group of 8 students was exposed
to a neutral message, “People are walking on the s eet.” All students participated in a
summer program designed to raise their math skilis, and all took the assessment test
again at the end of the program. liable 11.8 gives data on the subjects’ scores before
and after the program. (a) Is there good evidence that the treatment brought abouta greater improvement in
math scores than the neutral message? State hypotheses, carry out a test, and state your
conclusion. Is your result signiﬁcant at the 5% level? At the lU% level? Chapter Review 5?? 1) 678 Chapter 11 Inference for Distributions TABLE 11.3 Mathematics skills scores before and after a subliminal message Treatment Group Controi Group
Protest Post~te5t Protest Post—test 18 24 18 29
18 25 24 29
2] 33 20 24
18 29 18 26
18 ' 33 24 38
20 36 22 27
23 34 15 22
23 36 19 31
21 34 17 27' Source: Data provided by Warren Page, New York City
Technical College, from a study done by John Hudcsman. (b) Give a 90% confidence interval for the mean difference in gains between treat—
ment and control. a 11.59 STRESS RMDNE PHS AND FRIENDS Stress is a fact of everyday life. Researchers explored
how the presence of others can affect certain stress indicators when a person performs a
stressful task. In this study, the researchers asked 45 women to perform mental arithmetic
in the presence of their pet dog (P), a good female friend (F), or alone (C, for control). To
record the participants’ stress levels during the task and rest periods, the experimenters
measured maximum heart rate (beatsfininute). The researchers were interested in esplor—
ing whether the fact that a human friend could evaluate the subject’s performance at arith—
metic while a dog could not would affect the participant’s stress level.3U Condition Max.heartrate I Condition Max.heartrate I Condition Max.heartrate c 115 P 128 a P 72
e 110 P 122 P 72
e 113 I P 103 P 74
c 103 P 128 P 68
c 114 P 131 P 61
c 112 P 118 P 82
c 115 P 83 a P 72
c 96 P 127 l P 78
c 107 P 132 p P 92
e 103 I P 103 P 127
c 95 P 126 i P 87
e 113 , P 116 i P 73
c 120 P 110 l P 74
e 96 P 11.3 P 76
c 34 P 120 P 70 Use these data to examine the researchers’ question of interest If you ﬁnd statistically
significant difference between two of the groups, estimate the size of that difference. 11.70 You look up a census report that gives the poPulations of all 92 counties in the
state of Indiana. Is it proper to apply the one—sample t method to these data to give a
95% confidence interval for the mean pOpulation of an Indiana county? Explain your
answer. 11.?1 Exercise 1.28 (page 35) gives 29 measurements of the density of the earth, made
in 1798 by Henry Cavendish. Display the data graphically to check for skewness and
outliers. Then give an estimate for the density of the earth from Cavendish’s data and
a margin of error for your estimate. 11.72 CHOLESTEROL 1N DUES High levels of cholesterol in the blood are not healthy in
either humans or dogs. Because a diet rich in saturated fats raises the cholesterol level.
it is plausible that dogs owned as pets have higher cholesterol levels than dogs owned
by a veterinary research clinier “Normal” levels of cholesterol based on the clinic’s dogs
would then be misleading. A clinic compared healthy dogs it owned with healthy pets
brought to the clinic to be neutered. The summary statistics for blood cholesterol lcxL
cls (milligrams per deciliter of blood) appear below.31 Group :1 i 5 Pets 26 193 68
Clinic 23 174 44 (a) ls there strong evidence that pets have higher mean cholesterol level than clinic
dogs? State the H U and H d and carry out an appropriate test. Give the P—value and state
your conclusion. (1)) Give a 95% confidence interval for the difference in mean cholesterol levels
between pets and clinic dogs. (c) Give a 95% conﬁdence interval for the mean cholesterol level in pets. (d) What conditions must be satisﬁed to justify the procedures you used in (a), (b),
and (e)? Assuming that the cholesterol measurements have no outliers and are not
strongly skewed, what is the chief threat to the validity of the results of this study? 11.73 ACTIVE VERSUS PASSIVE LEARNING A study of computer—assisted learning exalrlincd
the learning of “Blissymbols” by children. Blissymbols are pictographs (think of
Egyptian hieroglyphs) that are sometimes used to help leaminguimpaired children
connnunicate. The researcher designed two computer lessons that taught the same
content using the same examples. One lesson required the children to interact with
the material, while in the other the children controlled only the pace of the lesson.
Call these two styles “Active” and “Passive.’1 After the lesson, the computer presented
a quiz that asked the Children to identify 56 Blissymbols. Here are the numbers of cor—
rect identiﬁcations by the 24 children in the Active group:32 29 28 24 31
24 35 21 24 44 28 15 24 27 23 20 22 23 21
17 21 21 20 28 16 Chapter Review 679 EBB Chapterll lnferenceforDistrihutions The 24 children in the Passive group had these counts of correct identiﬁcations: 16 14 17 15 26 I? 12 25 2] 20 18 21
20 16 18 15 26 15 13 17 21 19 15 12 (a) Is there good evidencc that active learning is superior to passive learning? Give
appropriate statistical justiﬁcation for your answer. (13) Give a 90% conﬁdence interval for the mean number of Blissymbols identified
correctly in a large population of children after the Active computer lesson. ...
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