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Unformatted text preview: (revised 11/08/06) 2201/Quiz 03 Page 1 of 6 Louisiana State University EXST 2201 Quiz 03 _ Fall 2006 Name: E Y Section: Score: Due: Week of Nov 13 2006 (100 pts) Directions: Put your answer (letter) in the associated blank. You may use any book and talk
to any person. You do not have to show your work to get credit. 1. General : Classify the following scenarios. A. Sample 1: The weights (lbs) of 19 newborn females. 6 (2 pts)
Sample 2: The weights (lbs) of 19 newborn males.
a) Paired—samples. b) Independent samples. B. Sample 1: The scores (points) of 13 students who took the ACT. 13 (2 pts)
Sample 2: The scores (points) of 13 other students who took the SAT.
a) Pairedsamples. b) Independent samples. C. Sample 1: The pre—training weights (lbs) of 17 athletes. A (2 pts)
Sample 2: The posttraining weights (lbs) of the same 17 athletes.
a) Pairedsamples. b) Independent samples. 2. Paired—Sample: A weightlifting coach claims that weightlifters can increase their
strength by taking a certain supplement. To test his theory, the coach randomly selects 9
athletes and gives them a strength test using a bench press. Thirty days later, after regular
training using the supplement, they are tested again. The results are listed below. Test the
claim that the supplement is effective in increasing the athlete’s strength. Use
signiﬁcance 0.10 and assume that the data are distributed normally. @L Before: 215 240 188 212 275 260 225 200 182 B After: 225 245 188 210 282 275 230 195 190
Difference: 10 5 0 2 7 15 —5 5 —8
@ L ‘ 13 < O a dbar s 2
Difference: 9 —4.78 6.24
A. What is the appropriate set of hypotheses (H0, H1)? C (3 pts)
a) mu(d) = 0, mu(d) .ne. 0 b) mu(d) .ne. 0, mu(d) = 0
c) mu(d) = 0, mu(d) < 0 d) mu(d) = 0, mu(d) > 0
B. What is the correct value of the test statistic? A (3 pts)
2 a) 2.30 b) 6.51 . c) —4.44 d) —6.51 (revised 11/08/06) 2201/Quiz 03 Page 2 of 6 C. What is the correct Pvalue for this test statistic? A (3 pts)
a) 0.025 b) 0.050
c) 0.020 d) 0.100 D. Does the supplement signiﬁcantly increase the athlete’s strength? A (2 pts)
a) Yes. b) No.
c) Sometimes. d) Depends on distribution. 3. T woSample: A study was conducted to determine if the salaries of elementary school
teachers from two neighboring districts were equal. A sample of 15 teachers from each
district was randomly selected. Test the claim that the salaries from both districts are
equal. Use signiﬁcance 0.05 and assume that the data are distributed normally. a xbar s
District 1: 15 $28,900 $2,300
District 2: 15 $30,300 $2,100
A. What is the appropriate set of hypotheses (H0, H1)? A (3 pts)
a) mu(1) — mu(2) = 0, mu(1) — mu(2) .ne. 0
b) mu(1) — mu(2) .ne. 0, mu(1)— mu(2) = 0
c) mu(1) — mu(2) = 0, mu(l) — mu(2) < 0
d) mu(1) — mu(2) = 0, mu(1) — mu(2) > 0
B. What is the correct conﬁdence interval? D (3 pts)
a) (2475, —325) b) (—2100, —700)
c) (—2975, 175) d) (3125, 325)
C. Are the teacher’s salaries from the two districts different? ES (2 pts)
21) Yes. b) No.
0) Sometimes. d) Depends on distribution. 4. TwoProportion: In the initial test of the Salk vaccine for polio, 400 children were
selected and divided into two groups of 200. One group was vaccinated with the Salk
vaccine while the second group was vaccinated with a placebo. Of those vaccinated with
the Salk vaccine, 33 later developed polio. Of those vaccinated with the placebo, 115
later developed polio. Test the claim that the Salk vaccine is effective in lowering the rate
of polio. Use signiﬁcance 0.01 and assume that the data are distributed normally. A. What is the appropriate set of hypotheses (H0, H1)? C (3 pts)
a) p(salk) —p(placebo) = 0, p(salk) —p(placebo) .ne. 0
b) p(salk) —p(placebo) .ne. 0, p(salk) —p(placebo) = 0
c) p(salk) —p(placeb0) = 0, p(salk) —p(placebo) < 0 d) p(salk) —p(placebo) : 0, p(salk) —p(placebo) > 0 (revised 11/08/06) 2201/Quiz 03 B. What are the correct proportions (p(salk), p(placebo)) ?
a) 0.095, 0.435 b) 0.575, 0.165
c) 0.165, 0.575 d) 0.435, 0.095 C. What is the correct value of the test statistic?
a) 0.23 b) 1.38
c) 9.54 d) 8.49 D. What is the correct conﬁdence interval?
a) (—0.52, 0.30)
c) (0.53, 0.30) b) (—0.30, 0.52)
d) ( 0.30, 0.53) E. Was the Salk vaccine effective at reducing the rate of polio?
a) Yes. b) No.
0) Sometimes. d) Depends on distribution. 5. ANOVA Logic: A. How many populations (columns of data) is ANOVA used for?
a) 0 b) 1
c) 2 d) 3 or more B. What statistical distribution does ANOVA use to make a decision?
a) 2 Distribution b) F Distribution
0) p Distribution (1) t Distribution C. In a oneway ANOVA a factor can have only one level?
a) Always b) Never
0) Sometimes d) It depends D. What is the null hypothesis in a oneway ANOVA with three populations?
a)#1=#2=#3 b)#1¢#2=#3
c) #1=#2¢#3 d) #1¢#2¢,Us E. Which of the following is NOT an assumption of ANOVA? a) Random samples. b) Dependent samples.
0) Normally distributed. (1) Equal standard deviations. Page 3 of 6 C (3 pts) D (3 pts) _/‘\_ (3 pts) L (2 pts) L (2 pts) _A_ (2 pts) _& (2 pts) (revised 11/08/06) 2201/Quiz 03 6. ANOVA Method: A. The AN OVA method consists of:
1) An overall test of population means; and
2) Follow up analysis giving speciﬁc details?
a) True b) False
0) Sometimes d) It depends B. The F —statistic is computed as a ﬁaction with the variation _A_ in
the numerator and with the variation _B_ in the denominator?
a) A = Between samples B = Within means
b) A = Within samples B = Between means
0) A = Between means B = Within samples d) A = Within means B = Between means C. The total sum of squares (SST oral) can be decomposed as:
a) SSModel * SSError b) SSModel — SSError
c) SSModel / SSError d) SSModel + SSError D. The Fstatistic in ANOVA is computed as:
a) SSModel * SSError
b) SSModel / SSError
c) SSModel  SSError
d) None of the above. B. What are the correct values to ﬁll the two blanks LA_ and _B__)
in the ANOVA table below? Sum of Mean Page 4 of 6 _A. (3 pts) C (3 pts) D (3 pts) L (3 pts) Source DF Sguares Sguare FValue PValue Model 2 246 123
Error _A_ 1 160 29
Corrected Total 42 1406 a)A=40,B= 4.24
c)A=44,B=94 b)A=42,B=152
d)A=40,B= 0.24 P (revised 11/08/06) 2201/Quiz 03 Page 5 of 6 7. AN 0 VA Extra: A. For a signiﬁcance level 0.05, a P—value of 0.025 in an ANOVA means
that the data give evidence that the means of all populations are equal? 8 (3 pts) a) True b) False
0) Sometimes d) It depends
B. Which of the following adjustment methods are only valid for
pairwise comparisons (comparing only two means)? A B (3 pts)
a) Bonferroni b) Tukey
c) Scheffe d) Wilcoxon
C. Which of the following is the correct Bonferroni adjustment to make
five comparisons at an overall experimental error rate of 0.05? C (3 pts)
a) acomparison = acamparison : c) ammparim = 0.01 (1) None of the above D. Which population means can be considered signiﬁcantly different in the Tukey Grouping shown below? A (3 pts)
a) 1,3and5 b)2and4
c)3and5 d)1,2,3and4
Population Mean Tukey Grouping
3 17.95 A
2 15.25 A B
4 12.80 A B
1 1 1.15 B
5 9.05
E. Statistical power measures the ability to reject the null hypothesis
when the null hypothesis does not reﬂect the truth? A (3 pts)
a) True b) False
c) Sometimes d) It depends
F. Increasing the sample size will decrease the power of a test? B (3 pts)
a) True b) False c) Sometimes d) It depends (revised 11/08/06) 2201/Quiz 03 Page 6 of 6 Scenario: Concrete Strength.
An engineer wants to know if the strength of two separate concrete mixes are different.
He randomly selects 9 cylinders of mixture 670301 (sample #1) and 10 cylinders of
mixture 670400 (sample #2). After 28 days, he measures the strength (in pounds per
square inch) of the 6 by 12 inch cylinders and obtains the information below. Use
signiﬁcance level 0.05.
BOXp10t= all points inside fences.
Normal probability plot = all points inside bounds. Sample E Q i .3
670301 1 9 3,669 458.5
670—400 2 10 4,483 473.7
A. What is the appropriate test procedure? 8 (3 pts) a) Two—sample z—test of the mean. b) Twosample t—test of the mean.
c) Twosample z—test of proportion. d) Pairedsample t—test of the mean. B. What is the appropriate set of hypotheses(H0, H1)? A (3 pts) ‘
a) mu(1) — mu(2) = 0, mu(1) — mu(2) .ne. 0
b) mu(1) ~ mu(2) .ne. 0, mu(1) — mu(2) = 0
c) mu(1) — mu(2) = 0, mu(1) — mu(2) < 0
d) mu(1) — mu(2) = O, mu(1) — mu(2) > 0 C. What is the correct magnitude of the critical value? D (3 pts)
a) 2.110 b) 2.093
c) 1.734 d) 2.306 D. What is the correct value of the test statistic? p C (3 pts)
a) 1.96 b) +3.80
0) —3.80 d) +0.018 B. What is the correct conﬁdence interval? 9 (3 pts)
a) (904, 473) b) (1307, —321)
c) (1061, 567) d) (1061, 567) F. Are these concrete mixes signiﬁcantly different in strength? A (3 pts)
a) Yes. b) No. c) Sometimes. d) Maybe. ...
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