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Final Statistics Examination for Statistics 486
Name _______________________________________________________________________
Figure 1: Regular season wins for the New England Patriots, 2002-2003.
1. The New England Patriots improved 56% in wins between 2002 and 2003. What is wrong
with Figure 1?
________________________________________________________________________
2. TABLE 1Distribution of Items Sold at Garage Sale
Class Interval Frequency
Table 1 and the histogram shows the distribution of the number of items sold at a
1
$1-$5
8
garage sale. Suppose that after the garage sale, you want to determine which items
2
$6-$10
6
3
$11-$15
4
$16-$20
2
5
$21-$25
4
6
$26-$30
7
$31-$35
were the most popular: the high-priced items, the low-priced items, and so forth.
Let's say you sold a total of 32 items for the following prices: $1, $2, $2, $2, $5, $5,
$5, $5, $7, $8, $10, $10, $10, $10, $11, $15, $15, $15, $19, $20, $21, $21, $25, $25,
$29, $29, $29, $30, $30, $30, $35, $35.
a. Fill in the two missing frequencies. Class 3_____________ , Class 6 _____________
b. The shape of this distribution (using the histogram) is called
2
________________________________________ (normal, positive skew, negative skew,
bimodal, etc.)
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3. Write the definitions of descriptive or inferential statistics using Genus and Difference.
Descriptive ___________________________________________________________
_____________________________________________________________________
Inferential ____________________________________________________________
_____________________________________________________________________
4. The correlation between a person’s hair length and score on the midterm is very nearly
zero. If your friend has a crewcut, your best guess as to what he got on the midterm is:
a. The standard deviation of scores on the midterm
b. The mean minus the standard deviation
c. The mean plus the standard deviation
d. The mean score
5. Suppose the mean on the final exam is 24 (out of 40), with a standard deviation of 1.5. If
you get a 21, how well did you do (relative to the rest of the class), assuming it’s roughly a
normal distribution?
a. Very poorly—perhaps the lowest score
b. Not well, but somewhere near the average
c. OK—about average
d. Nicely—better than the median
6. In a true normal frequency distribution
a. The mean always is the same as the standard deviation
b. The mean is never the same as the mode
c. The mode is never the same as the median
d. The mean always is the same as the median
7. In a class of 100, the mean on a certain exam was 50, the standard deviation was 0. This
means:
a. Half the class had scores less than 50
b. There was a high correlation between ability and grade
c. Everyone had a score of exactly 50
d. Half the class had 0’s and half had 50’s.
8. The error made by researchers who reject the null hypothesis when it is, in fact, correct is
called ______________________________
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9. Which one of the following variables is not nominal?
a. Age of a person
b. Gender of a person: male or female
c. Choice on a test item: true or false
d. Marital status of a person: single, married, divorced, other
10. Which one of these statistics is unaffected by outliers?
a. Mean
b. Interquartile range
c. Standard deviation
d. Range
11. The value of a correlation is reported by a researcher to be r = -.5. Which of the following
statements is correct?
a. The x-variable explains 25% of the variability in the y-variable.
b. The x-variable explains -25% of the variability in the y-variable.
c. The x-variable explains 50% of the variability in the y-variable.
d. The x-variable explains -50% of the variability in the y-variable.
12. Which of the following is not a measure of variability?
a. Range
b. Variance
c. Standard deviation
d. Sampling error
13. Every other customer entering a shoe store was given a different coupon. One coupon
offered a second pair of shoes for 50% off. The other coupon offered to reduce the total
price by 25% if two pairs of shoes were purchased. The purpose was to determine which
coupon was more effective in getting individuals to buy two pairs of shoes. In this
experiment, what is the independent variable? __________________________________
14. Assume the monthly income of college students are normally distributed with the mean of
$500 and a standard deviation of $55.
a. Discuss what information is available from these two figures?
 ______________________________________________________________
 ______________________________________________________________
 ______________________________________________________________
b. What is the z-score of Student A if she earns $495 a month? ___________________
c. What percent of college students earn less than Student A? ____________________
d. How many standard deviations from the mean is Student A? __________________
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15. Following are two scattergrams (in Figure A and in Figure B). Four different correlation
coefficients are listed under each scattergram. Choose the coefficient that best matches
each scattergram.
16. Using the table in the textbook or Excel, convert the following z-scores to percent below:
z-score
% below the z-score
1.10
4.30
0 .05
-2.80
-0.5
-1.96
17. You have just calculated the average and standard deviation of a list of 101 numbers,
finding an average of 240.0 and a standard deviation of 25.88. Unfortunately, a check of
the list of numbers uncovers two errors.
A number originally listed as 230 should be 200.
A number originally listed as 250 should be 280.
Based on this information, you decide:
(a) It will be impossible now to give either the correct value of the mean or the correct
value of the standard deviation.
(b) The mean will remain at 240, and the standard deviation will increase.
(c) The mean will remain at 240, and the standard deviation will decrease.
(d) The mean will change, but the value of the standard deviation will remain unchanged.
(e) The mean and standard deviation will remain at 240 and 25.88, respectively.
18. To analyze data measured on a nominal scale, researchers should use parametric or
nonparametric statistics. _________________________________________________
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19. Suppose you read that t = 2.00, df = 20, p > .05 for the difference between two means.
Using conventional standards, should you conclude that the null hypothesis should be
rejected? (yes or no and then why)____________________________________________
20. Suppose you read that t = 2.85, df = 40, p < .05 for the difference between two means.
Using conventional standards, should you conclude that the null hypothesis should be
rejected? (yes or no and then why)___________________________________________
21. When a researcher uses a large sample, is he or she “more likely” or “less likely” to reject
the null hypothesis than when a researcher uses a small sample? ______________
22. When the size of the difference between means in a t-test is large, is a researcher “more
likely” or “less likely” to reject the null hypothesis than when the size of the difference is
small? __________________________________________________________________
23. When the amount of variation in the population is very homogeneous (has little
variability), is a researcher “more likely” or “less likely” to reject the null hypothesis than
when the amount of the variability is large? ____________________________________
24. In a z test for a single sample, the sample’s mean is compared to the population’s ______.
25. When we want to compare whether girls’ scores on the SAT are different from boys’
scores, we should use a t test for (dependent samples or independent samples)_________.
26. Match the coefficient of determination and the diagram illustrating this correlation.
27. If x̄ = 75 points, s = 7 points, n = 100, then the SEM = __________________________
95% CI levels= ___________________ points and ____________________ points
95% CI ± ________ points
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28. A research study was conducted of Social Traits of hearing-impaired students.
Participants were 220 hearing-impaired adolescents enrolled in 15 large public schools
programs throughout the United States and in one Canadian metropolitan area.
Participants were in the high school part of the program.
Table 1: Means and Standard Deviations
Subscale
School Participation
With hearing-impaired students
With hearing students
Social Activities
With hearing-impaired students
With hearing students
Emotional Security
With hearing-impaired students
With hearing students
M
SD
19.5
17.4
5.1
5.1
18.5
19.0
5.6
5.5
22.2
21.6
3.7
3.8
Notes: N for all subscales was 220. (Higher averages indicate more of the trait in
questions.)
a. What is the SEM for “School Participation with hearing-impaired students”? _______
b. What is the 68% confidence interval for “School Participation with hearing-impaired
students”? ___________________________________________________________
c. What is the 95% confidence interval for “School Participation with hearing-impaired
students”? ___________________________________________________________
29. The following are excerpts on sampling from real research. Identify the nonrandom and
random sampling events.
a. Researchers state, “For the analyses, we used a sample of Norwegian 13-year-od
students (N= 1,736; 49% were girls) and15-year-old students (N= 1,622; 51% were
girls). The students were selected using a stratified, systematic sampling procedure,
thus yielding a nationally representative sample.”_____________________
b. Researchers state: “A total of 102 U.S. and 102 Japanese men participated in this
study. The U. S. participants were recruited from an undergraduate student research
pool in the psychology and educational psychology departments at a large public
university in the Rocky Mountain region of the United States.”________
c. Researchers state: “A sample of 60 was randomly selected from 125 people arrested
on DWI offenses and referred by the county to a professional evaluator between May
2000 and December 2003.” __________________________________________
d. Researchers state: “Smokers (defined as individuals smoking 10 or more cigarettes
per day) were approached at various locations on or near the University of Pittsburgh
campus. The sample (N= 102) included 42 men and 60 women, with an average age
of 27.78.” _____________________________________________
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30. Participants in this study were a volunteer sample of full-time undergraduate students at a
small, private, liberal arts college in the South. The researchers measured depression, selfesteem, and social connectedness. A Pearson r was used to determine if there was any
relationship between the measured values.
Table 1
Pearson’s Product Moment Correlations Between the Dependent Measures (n=227)
Measure
Depression
Social connectedness
Self-esteem
-.372
.414
Depression
-.619
a. What is the value of the correlation for the relationship between Depression and Selfesteem? _________________________________________________________________
b. What is the value of the correlation for the strongest relationship in the table? _________
The Five Chapters in a Research Paper
31. A description of how the sample that was used in the study was selected is likely to
be found in the ____________________ chapter of a research paper.
32. The most comprehensive rationale for the study is likely to be found in the
_____________
chapter of a research paper.
33. The statistical findings of the study are presented in detail in the ______________
chapter.
34. Suppose that you wish to estimate the weight of the UM football team by taking a
single sample, known as a “point estimate.” You select 30 players at random and find the
average weight is 218 pounds and you fortunately happen to know the team standard
deviation is 11.5 pounds.
a. What is the point estimate of the population mean?_______________________
b. What is the weakness of this method?_________________________________
c. It might be better to find a range, i.e., a confidence interval (interval estimate), in
which we could say with a given confidence that the sample average is approximately the
team average. So, find a confidence interval that will include the team mean 68% of the
time.
______________________________________________________________
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35. A study by a local real estate board sampled nine realtors who serve the Missoula
market, measuring for each realtor the numbers of houses sold in February 2007 and in
February 2008.
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean
Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Feb 2007
12.55555556
63.27777778
9
0.96053484
Feb. 2008
8.555555556
31.52777778
9
0
8
4
0.001974886
1.859548033
0.003949773
2.306004133
What is the decision based on the two-tailed critical value?
(a) Reject H0.
(b) Fail to reject H0.
(c) Impossible to determine.
Interpret the decision.
(a) There is sufficient evidence to show that the mean number of sales per realtor is less
in Feb. 2007 than in Feb. 2008.
(b) There is insufficient evidence to show that the mean number of sales per realtor is
less in Feb. 2007 than in Feb. 2008.
(c) There is sufficient evidence to show that the mean number of sales per realtor is
greater in Feb. 2007 than in Feb. 2008.
(d) There is insufficient evidence to show that the mean number of sales per realtor
is greater in Feb. 2007 than in Feb. 2008.
(e) None of the answers is correct.
36. A high school teacher is interested in comparing the spelling performance of students in two
different classrooms.
a. What is the independent variable (IV)? ____________________________________
b. What is the dependent variable (DV)? ____________________________________
c. What is the level of measurement for the IV in this independent t-test? __________
d. What is the level of measurement for the DV in this independent t-test? _________
e. What statistical test would be appropriate? (dependent t-test, independent t-test, etc.)
_______________________________________
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37. Market researchers use the number of sentences per advertisement as a measure of
readability for magazine advertisements. A random sample of the number of sentences found in
30 magazine advertisements is listed. Use this sample to find the point estimate for the
population mean μ.
16 9 14 11 17 12 99 18 13 12 5 9 17 6 11 17 18 20 6 14 7 11 12 5 18 6 4 13 11 12
1. Point estimate_____________________________ sentences
2. 95% CI = ___________________ sentences ± ______________________ sentences
38. This test is also known as goodness of fit:
a. One-sample chi-square
b. Two-sample chi-square
c. Any nonparametric statistical test
d. Fisher’s exact test
39. Nonparametric statisitics might be preferred when:
a. Your sample size is very small
b. Your sample size is very large
c. The variables you are analyzing are continuous
d. All the assumptions of parametric statistics have been met
Last Question!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Table 1
Variable 1
Mean
Variance
Observations
Pooled Variance
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
5
4.266666667
16
4.991666667
0
30
1.424212286
0.082352234
1.697260851
0.164704468
2.042272449
Variable 2
3.875
5.716666667
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P a g e | 10
Suppose a researcher hypothesizes that people who are allowed to sleep for only four hours will
score significantly lower than people who are allowed to sleep for eight hours on a cognitive
skills test. She brings 32 participants into the sleep lab and randomly assigns them to one of two
groups. In one group (Variable 1) she has participants sleep for eight hours and in the other
group (Variable 2) she has them sleep for four. The next morning she administers the Cognitive
Ability Test (CAT) to all participants. (Scores on the CAT range from 1-9 with high scores
representing better performance.)
Non-directional research question__________________________________________________
Research design________________________________________________________________
Population (number)____________________________________________________________
Sample (number)_______________________________________________________________
Variables: Independent ________________ Dependent _______________________________
Levels of Data: Independent ____________ Dependent _______________________________
Null hypothesis_________________________________________________________________
Definitions of the Null hypothesis: For the purposes of this research, experimental importance
will be defined as three (3) points on the difference in the means of the CAT score.
Experimental consistency will be set at alpha = .05.
Statistical procedure ____________________________________________________________
Degrees of freedom=
________________________________________________________________________
a priori _______________________________________________________________________
Observed value of t _________________________ Critical value of t _____________________
Results_______________________________________________________________________
Determination of the null hypothesis _______________________________________________
P a g e | 11
______________________________________________________________________________
______________________________________________________________________________
Reject the null or fail to reject the null? __________________________________________
What does this mean about the number of hours slept and the scores on the CAT? ___________
_____________________________________________________________________________
_____________________________________________________________________________