STA 3024 Fall 2005 Exam 2
PRINT Name ______________
1) Among a sample of 1000 U.S. school aged children, 50 have a particular condition.
Among a sample of 500 Canadian children, 10 have the condition.
a) Give the estimated relative risk (U.S. relative to Canada).
^
pUS 
50
 0.0500
1000
^
pC 
10
 0.0200
500
RR 
0.05
 2.5
0.02
b) Give a 95% confidence interval for the population relative risk.
1  0.05 1  0.02

 0.3421
1.96   0.6704
50
10
95% CI : 2.5e  0.6704,2.5e0.6704  (1.2788,4.8876)
 


c) Based on your confidence interval, give the best conclusion (0.05 significsnce level).
i.
Cannot conclude risks differ between U.S. and Canada
ii.
Conclude higher risk in U.S.
iii.
Conclude lower risk in U.S.
2. A clothing manufacturer is interested in purchasing a new machine to sew jeans. They
use their old machine to sew 30 pairs, of which 5 had irregularities and they use the
new machine to sew 30 pairs, of which 2 had irregularities. Write out all contingency
tables, conditional on these sample sizes and number of defects that give as strong or
stronger evidence in favor of the new machine having a lower irregularity rate than
the old machine.
Old
New
Total
Irreg
5
2
7
Not Irreg
25
28
53
Total
30
30
60
Old
New
Total
Irreg
6
1
7
Not Irreg
24
29
53
Total
30
30
60
Old
New
Total
Irreg
7
0
7
Not Irreg
23
30
53
Total
30
30
60
3. A consumer is interested in comparing prices among 3 grocery store chains in his
city. He randomly samples 10 branded products and obtains the regular price of each
product at each store. He finds that between store variation accounts for 25% of the
total variation and between product variation accounts for 60% of the total variation.
(a) Complete the following ANOVA table.
Source
DF
SS
MS
Fobs
Stores
3-1=2
.25(800)=200
100
100/6.6667=15
Products
10-1=9
.6(800)=480
53.33
Error
2(9)=18
800-680=120
6.6667
Total
30-1=29
800
(b) Test whether we can conclude that the population mean prices differ among the three
stores by completing the following sentence (use =0.05 significance level and circle
any correct bold type options and fill appropriate numeric values in the blanks).
Conclude / Do Not conclude means differ since 15 is above / below 3.555
(c) This is an example of dependent samples because (circle the best answer):
i.
The sample sizes for each store are the same
ii.
The same products are observed at each store
iii.
There are 3 stores
4. An advertising executive wants to compare the effectiveness of 3 ads. She samples 18
consumers, and assigns (randomly) 6 to ad 1, 6 to ad 2, and 6 to ad 3. She has each
consumer rate their likelihood on a scale of 0 to 100 their purchase intentions of the
product. The ratings are given below.
(a) Compute the Kruskal-Wallis statistic.
Ad 1
15 (1)
23 (2)
27 (3)
35 (4)
48 (6)
50 (8)
Ad 2
36 (5)
49 (7)
55 (9)
64 (10)
68 (12)
70 (13)
Ad 3
65 (11)
72 (14)
78 (15)
80 (16)
85 (17)
90 (18)
R1  24 R2  56 R3  91
12  (24) 2 (56) 2 (91) 2 
H



  3(19)  70.13  57  13.13
18(19)  6
6
6 
(b) Can we conclude the population distributions of purchase intentions differ at =0.05
significance level? Yes / No Why? 13.13 above / below 5.991
5. Ford wants to compare mean assembly times for Explorer’s at their 3 assembly
plants. They observe random samples of 21 cars at each plant, and obtain the
following summary statistics on assembly times (in minutes):
Plant
Mean
Std. Dev.
Atlanta
80
8
Chicago
85
10
Detroit
75
11
(a) Compute the between plant (Group) sum of squares and its degrees of freedom


x  80 SSG  21 (0)2  (5)2  (5)2  1050
dfG  3  1  2
(b) Compute the within plant (Error) sum of squares and its degrees of freedom


SSE  (21  1) (8)2  (10)2  (11)2  5700
df E  63  3  60
(c) Compute the test statistic
Fobs 
(1050 / 2)
 5.53
(5700 / 60)
(d) Conclude population means differ ( if the test statistic is above / below 3.150
6. For the CRD: E ( MSG )   2 
 n (
i
i
  )2
E ( MSE )   2 Rank the following
I 1
cases from lowest (1) to highest (3) for what we would “expect” the F-statistic to be:
i.
n1 = n2 = n3 = 10
2 (ratio=3.5)
ii.
n1 = n2 = n3 = 20
3 (ratio=41)
iii.
n1 = n2 = n3 = 5
1 (ratio=1.1)
7. A researcher is interested in comparing married men’s and women’s attitudes toward
same-sex marriage. A random sample of 1000 married couples is obtained. Of these
couples, both the male and female opposed it for 200 of the couples, both the male
and female favored it for 300 of the couples. The male favored and the female
opposed it for 280 of the couples. For the remaining couples the male opposed and
the female favored.
(a) Give the test statistic for testing whether the proportions of males and females
favoring same sex marriage are the same (H0) or differ (HA)
M \ F
Favor
Oppose
Total
z obs 
Favor
300
220
520
280  220
280  220
Oppose
280
200
480
Total
580
420
1000
 2.68
(b) What do we conclude at the =0.05 significance level?
i.
Do not conclude the proportions differ
ii.
Conclude a higher proportion of males favor same-sex marriage
iii.
Conclude a higher proportion of females favor same-sex marriage
8. A Randomized Block Design is used to compare 3 types of sounds on sleep in 8
people suffering from sleeping disorders. Each subject is assigned to each sound type
(in random order) and the time until the person falls asleep is measured The
following calculations are obtained from a statistical software program.
x1  45 x 2  65 x 3  50 MSE  100
Use Bonferroni’s method to obtain simultaneous 95% confidence intervals for all pairs of
population means. Give the correct conclusion based on the intervals (NSD=”Not
significantly different).
Sounds
Point Estimate
Confidence Interval
Conclude
1 vs 2
45-65 = -20
(-33.6 , -6.4)
1 < 2
1 vs 3
45-50 = -5
(-18.6 , 8.6)
NSD
2 vs 3
65-50=15
(1.4 , 28.6)
2 > 3
t **  2.718
2
SE ( x i  x j )  100   5
8
t * *SE  13.6
9 A study is conducted to find possible risk factors for a personality disorder. A sample
of 500 children with the disorder is obtained, and a sample of 500 control children
with similar demographic conditions (but not the personality disorder) is obtained.
Mothers were asked whether they consumed alcohol during their pregnancies. The
appropriate measure(s) of association to report would be:
a) Relative Risk and Odds Ratio
b) Relative Risk, but not Odds Ratio
c) Odds Ratio, but not Relative Risk (retrospective study)
d) Neither Relative Risk or Odds Ratio
10 A study is conducted comparing three methods of training subjects to draw. The
experiment is conducted as a Completely Randomized Design, with 20 subjects in
condition 1, 15 subjects in condition 2, and 18 subjects in condition 3. The
researchers conclude (correctly) that the effects of the training methods are not equal
at the 0.05 significance level and decide to use Bonferroni’s method to obtain
simultaneous 95% confidence intervals for all pairs of conditions.
a) Give the appropriate critical value (t) they will use to obtain the intervals
2.477
b) Which interval will be narrowest? Which will be widest? Circle the best answer.
i. Narrowest: Condition 1 vs Condition 2
Widest: 2 vs 3
ii. Narrowest: Condition 1 vs Condition 3
Widest: 2 vs 3
iii. Narrowest: Condition 2 vs Condition 3
Widest: 1 vs 3
iv. Narrowest: Condition 2 vs Condition 3
Widest: 1 vs 2
v. We need more information
11 Friedman’s test is being conducted in an experiment with 4 treatments, each being
applied to 8 blocks. You wish to be sure that your rankings “add up” properly. What
will the total of the rank sums equal?
Within each block, ranks sum to 1+2+3+4=10
8 Blocks means total is 8(10) = 80
12 Researchers in a law journal published means and standard deviations of exit
velocities of bullets from 4 types of handguns. Unfortunately, they did not give the
sample sizes, so you can obtain the sums of squares only up to a constant involving
the sample sizes (assuming a balanced experiment). Give the rejection regions for
=0.05 level test of whether the velocities differ by gun type.
a) n1=n2=n3=n4=3 Conclude means not equal if Fobs  F.05,3,8 = 4.066
b) n1=n2=n3=n4=8 Conclude means not equal if Fobs  F.05,3,28 = 2.947
13 A study is conducted to compare the effects of 4 colors of paper on students’ ability
to complete a reading task. A sample of 10 students is selected and each is given
reading tasks on all four colors of paper (in random order with other tasks being
completed in between). The times are highly skewed (some times were very long
relative to the others). The most appropriate analysis for this experiment is:
a) Kruskal-Wallis Test
b) McNemar’s Test
c) Friedman’s Test
d) Fisher’s exact test
14 The following EXCEL output gives the results from a 1-way analysis of variance
(completely randomized design).
ANOVA
Source
Groups
Error
Total
df
2
147
149
SS
MS
F
P-value
1212.015 606.0075 2.206811 0.113684
40367.34 274.6078
41579.36
a) How many treatments (groups) were being compared? 2+1=3
b) How many individuals (subjects) participated? 149+1=150
c) The researchers conclude that the population group means are not all equal (at the
=0.05 significance level). Is their conclusion correct? Yes / No
I have not cheated on this exam _________________________________________
UFID _________________________________