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Psych 2101-Statistics ______________________
Exam 1 : 2/13/96
I. Multiple Choice: Choose the single best answer (2 points
each)_______
1. If the majority of students in this class know the material
thoroughly -- sothoroughly that they know the answers to almost
all the questions on this exam -- the distribution of exam scores
will probably be
a. Skewed positively XXb. Skewed negatively
c. Normallydistributed
2. In a distribution of scores for which the mean =65.5,
median=64 and mode=60, it was found that a mistake had been made
on one score. Instead of 70, the score should have been 90.
Consequently, which of the previously computed statistics shown
above would certainly be incorrect?
a. Median b. Mode XXc. Mean
3. The sum of deviation scores ( xi ) must equal 0 (within
rounding error). The sum of squared deviation scores ( xi 2 )
a. is always positive b. is not equal to zero c. can be
obtained by a shortcut
XXd. (all of the above are true)
4. As in the statistical example from Sir Ronald Fisher (Lady
Tasting Tea), it can
a. be proved that she can discriminate
XXb. not be proved beyond doubt that she can discriminate
c. be demonstrated better that she can discriminate if fewer
cups are used
d. be shown that taking a 5% chance of being wrong is never
acceptable
5. If Xi = 10, 11, 13; then X should be reported as
a. 11.333333
b. 11.3333
XXc. 11.33
d. 11
6. If we are trying to estimate the (unknown) binomial
population proportions, P and Q,by taking repeated samples from
the population (with replacement), and computing thesample's
proportions, p and q, then the best estimates we have for P and Q
are
a. the range of p and q from all the samples
b. the inclusive range p and q from all the samples
c. (p + q) / ã
XXd. The mean p and q of the samples
7. What is a distribution called when it has two most-frequently
occurring values?
a. Skewed b. Medianic XXc. Bimodal d.
Asymptotic
8. Skewness refers to the
a. flatness or peakedness of a distribution
b. heaviness of the tails of a distribution
c. modality of a distribution
XXd. lack of symmetry of a distribution
9. In a positively skewed distribution,
XXa. The mean is going to be towards the right of the
distribution
b. Mean = Mode = Median
c. The mean is going to be towards the left of the distribution
d. Most of the scores will be located at the right-hand end of
the distribution
10. In the new Boulder restaurant, Taco Bacanal, they also sell
burritos. In one day, 33people tried the Burrito Bestial, 25
ordered a Burrito Playero, and the winner was theBurrito
Parrandero, which was eaten by 55 pioneers. What is the
appropriate graphicalrepresentation for this kind of data?
XXa. Bar Graph b. Nomogram c. Frequency polygon
d. Histogram
11. In a fair draw from a fair (bridge) deck of cards, what is
the probability of drawing theQ ?
a. 1/4 b. 1/13 XXc. 1/52 d. 1.0
12. What is the probability of drawing any ?
a. 1/13 b. 1/52 XXc. 1/4 d. 1.0
13. If you draw a card, look at it, then replace it and draw one
more, what is theprobability that both were red?
a. 1/16 b. 1/8 XXc. 1/4 d. «
14. If you toss 4 coins, what is the probability that you will
get 4 Heads?
a. « b. 1/4 c. 1/8 XXd. 1/16
15. If you toss 4 coins, what is the probability that you will
get 2 Heads?
a. 2/16 b. 4/16 XXc. 6/16 d. 8/16
16. If the proportion P of white balls in an urn is .8 [i.e.,
P(W)=0.8] and the proportion Qof red balls is .2 [i.e.,
Q(R)=0.2], what is the probability of obtaining 5 white balls in
five successive draws (use replacement)?
a. .000327 b. .003276 c. .032768 XXd.
.327680
17. Assuming a flat distribution of birthdays across the year,
what is the probability of aperson's having a birthday in January
of a non-leap year?
a. 1/365 XXb. 31/365 c. 335/365 d. 62/365
18. Assume that you win the bet at the craps table if you throw
a 7 on your first roll of the two dice. What is the probability
of your throwing a 7 on your first try?
a. 3/36 XXb. 6/36 c. 9/36 d. 10/36
19. If the road between you and your destination makes a Y 3
times, and you havecompletely forgotten the directions, what is
the probability you will get there on your first try?
a.1/2 b. 1/4 XXc. 1/8 d.
1/16
20. If there are 25000 people on campus, including a total of
500 redheads, and assumingthat redheads are free to go anywhere
(I think they are), what is the probability that the next two
people you randomly encounter on campus will be redheads?
a. 1/50 XXb. 1/2500 c. 1/5000 d. 1/25000
II. Fill-in. Fill-in the blanks, as indicated. (Two points
each)
A special night is being held at the local dance club. It is
called "Random Dancing." Each person is assigned a number, and
all numbers are placed in a hat. You draw anumber from the hat,
and that chooses your dance partner. After each slip is drawn, it
isplaced back in the hat. Including yourself, there are 50
people in the dance club: 20 are men, 20 are women, and 10 are
androgynous. Of these, 9 have purple hair, 6 have nose rings, 5
have multiple tatoos, and 2 have pierced tongues. Assume
independence ofgender and attributes, unless otherwise indicated.
You are the first person to pick fromthe hat. What is the
probability that your first dance partner is
1. Yourself? ___
2. Is a woman? ___
3. Is a man with multiple tatoos? ___
4. Is androgynous and with pierced tongue? ___
5. Is either a man or someone with purple hair? ___
6. Is an androgynous man? ___
Suppose that you are again the first person to pick from the hat
for the second dance. What is the probability that:
7. You dance with the same person twice? ___
8. You dance with a man the first time and a woman the second
time? ___
9. At least one of your partners had multiple tatoos? ___
10. You will be home early? ___
III. Define the following and give an example of each (2 points
each):
1. Ordinal scale -
2. Continuous variable -
3. Population -
4. Conditional probability -
5. Measure of Central Tendency -
IV. True or False. (1 point each)
T or F 1. When K is a constant, ä(Xi + K) = äXi + K
T or F 2. When C is a constant, äCXi = CäXi
T or F 3. äX = nX
T or F 4. When C is a constant, äC = nC
T or F 5. äXi2 = (äXi)2
V. Graphs etc.
1. The following data' describe the total number of parking
tickets received in the last two years by a sample of medium-aged
drivers: 6, 7, 4, 6, 1, 10, 7, 5, 8, 3
From these scores, make a frequency distribution using a class
interval of 2, and then draw a histogram of the these grouped
data (10 points)
2. If a plot of raw-score reaction times looked like this:
Draw what a plot of deviation scores would look like, i.e.,
plot xi where xi = (Xi-)
(5 points)
5|
4| X
3| X X X
2| X X X X X
1| X X X X X X X
0|____________________
.3 .4 .5 .6
Seconds
3. Students at the University of Colorado at Boulder were
surveyed to estimate the extent of alcohol consumption among
college age females and males. One question asked the
respondents to indicate the numbers of beers/drinks each consumed
each week, onaverage. From these responses, means for men and
women were calculated, with the mean for men being 13.9 drinks
per week (Range = 0 - 40), and for women, 7.5 drinks per week
(Range = 0 -20).
a. Is the mean the best measure of central tendency for these
data? Explain your answer.
(4 points)
b. Given the further information that 50% of the women reported
an average of 0 drinks per week, while only 10% of men reported 0
drinks per week, make a likely histogram for women, and for men,
separately.
(6 points)