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Review problems, courtesy of Professors D. White-Durkin and J. Sukta.
1. Below is a bar graph of class representing a seminar containing seven students
who are either freshman, sophomores, juniors, or seniors. In the bar graph the bar
for the juniors has been omitted.
The number of students in the seminar who are juniors is:
A) 1 B) 2
C) 3 D) Cannot be determined from the information given.
Use the following to answer questions 2 - 3:
In a statistics class with 136 students, the professor records how much money each student has in their
possession during the first class of the semester. The histogram below shows the data
2. The percentage of students with under $10.00 in their possession is closest to
A) 44% B) 50% C) 60% D) 70%
E) None of These
3. The histogram
A) is skewed right.
B) is skewed left
C) is symmetric.
D) None of These
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Use the following information for problem 4 - 6.
A sample was taken of the salaries of 20 employees of a large company. The following are the
salaries (in thousands of dollars) for this year. For convenience, the data are ordered.
28 31 34 35 37 41 42 42 42 47 49 51 52 52 60 61 67 72 75 77
4. The mean salary for this year is
A) 42 B) 48 C) 48.5 D) 49.75
E) None of These
5. The median salary for this year is
A) 42 B) 48 C) 48.5 D) 49.75
E) None of These
6. The third quartile for the salaries for this year is
A) 34 B) 39 C) 48 D) 60.5 E) None of These
7. A penny is tossed and observed whether it lands heads up or tails up. Suppose the
penny is fair, i.e., the probability of heads is 1/2 and the probability of tails is 1/2.
This means
A) every occurrence of a head must be balanced by a tail in one of the next two or
three tosses.
B) If I flip the coin many many times the proportion of heads will be approximately
1/2, and this proportion will tend to get closer and closer to 1/2 as the number of
tosses increases.
C) regardless of the number of flips, half will be heads and half tails.
D) all of the above.
E) None of These
Use the following to answer questions 8 - 10:
If you draw an M&M candy at random from a bag of the candies, the candy you draw will have one of
six colors. The probability of drawing each color depends on the proportion of each color among all
candies made. Assume the table below gives the probability that a randomly chosen M&M has each
color.
Color
Probability
Brown
Red
Yellow
Green
Orange
Tan
0.3
0.3
?
0.1
0.1
0.1
8. The probability of drawing a yellow candy is
A) 0.1 B) 0.2 C) 0.3 D) impossible to determine from the information given.
E) None of These
9. The probability that I do not draw a red candy is
A) 0.1 B) 0.3 C) 0.7 D) 0.9 E) None of These
10. The probability that I draw either a brown or a green candy is
A) 0.1 B) 0.3 C) 0.4 D) 0.7 E) None of These
Use the following to answer questions 11 - 12:
Let X be the outcome of rolling a carefully made six-sided die. Assuming the die is fair, the probability
distribution for X is as follows.
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Value of x
1
2
3
4
5
6
Probability
1/6
1/6
1/6
1/6
1/6
1/6
11. The probability of rolling a value greater than three is
A) 1/6 B) 1/3 C) 1/2 D) 2/3 E) None of These
12. P(x < 2) has value:
A) 1/6 B) 1/3 C) 1/2
D) 2/3
E) None of These
13. Three people will be promoted from a pool of 24 eligible employees
(14 male and 10 females). What is the probability that exactly 2 females will
receive promotions.
A) 105 / 1012 B) 315 / 1012 C) 175 / 1728 D) 525 /1728 E) None of These
14. Event A has probability 0.4. Event B has probability 0.5. If A and B are disjoint,
then the probability that both events occur is
A) 0.0. B) 0.1. C) 0.2. D) 0.9. E) None of These
15. Suppose we roll a red die and a green die. Let A be the event that the number of
spots showing on the red die is three or less and B be the event that the number
of spots showing on the green die is more than three. The events A and B are
A) disjoint B) conditional C) independent D) reciprocals E) None of These
Use the following information for problems 16 - 17:
In a certain town, 50% of the households own a cellular phone, 40% own a pager, and 20% own both a
cellular phone and a pager.
16. The proportion of households that own neither a cellular phone nor a pager is:
A) 10%. B) 30%. C) 70%. D) 90%. E) None of These
17. The proportion of households that own either a cellular phone or a pager is:
A) 10%. B) 30%. C) 70%. D) 90%. E) None of These
Use the following to answer questions 18 - 21:
Consider the contingency table for adverse reaction to the lowering cholesterol medication Pravachol.
Medication
Pravachol
Placebo
Total
Heartburn
27
8
35
No Heartburn
873
392
1265
Total
900
400
1300
18. P(Taking Pravachol and experiencing heartburn)
A) 27 / 900 B) 900 / 1300 C) 27 / 1300 D) 927 / 2200
E) None of These
19. P(Taking Pravachol or experiencing heartburn)
A) 35 / 1300 B) 900 / 1300 C) 908 / 1300 D) 935 / 1300
20. P(Took Pravachol | Experienced heartburn)
A) 27 / 900 B) 27 / 400 C) 27 / 1300
D) 27 / 35
E) None of These
E) None of These
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21. P(Experienced heartburn | Took Pravachol)
A) 27 / 900 B) 27 / 400 C) 27 / 1300
D) 27 / 35
E) None of These
22. Suppose we roll a fair die four times. The probability that a six occurs on exactly
one of the rolls is
A) 0.0154 B) 0.3858 C) 0.0965 D) 0.0039 E) None of These
23. The law of large numbers states that, as the number of observations drawn at
random from a population with finite mean increases, the mean of the
observed values
A) gets larger and larger.
B) gets smaller and smaller.
C) gets closer and closer to the population mean .
D) fluctuates steadily between one standard deviation above and one standard
deviation below the mean.
E) None of These
24. The weight of reports produced in a certain department has a normal distribution
with mean 60g and standard deviation 12g. The probability that the next report
will weigh less than 45g is
A) 0.1056 B) 0.3944 C) 0.1042 D) 0.0418 E) None of These
Use the following to answer question 25:
A factory produces plate glass with a mean thickness of 4 mm and a standard deviation of 1.1 mm. A
simple random sample of 100 sheets of glass is to be measured, and the sample mean thickness of the
100 sheets,
, is to be computed.
25. The probability that the average thickness, , of the 100 sheets of glass is less
than 4.1 mm is
A) 0.8186. B) 0.3183. C) 0.1814. D) 0.6817. E) None of These
26. The distribution of actual weights of 8-oz. chocolate bars produced by a certain
machine is normal with mean 8.1 ounces and standard deviation 0.1 ounces. If a
sample of five of these chocolate bars is selected, the probability that their average
weight is more than 8 oz. is
A) 0.0125. B) 0.1853. C) 0.4871. D) 0.9875. E) None of These
Use the following information for problems 27 - 28:
An automobile insurer has found that repair claims have a mean of $920 and a standard deviation of
$870. Suppose that the next 100 claims can be regarded as a random sample from the long-run claims
process.
27. The probability that the average, , of the 100 claims is between $900 and
$1000 is
A) 0.091 B) 0.2302 C) 0.2302 D) 0.4122 E) None of These
28. The mean and standard deviation of the next 100 claims is
A) mean = $920 and standard deviation = $87.
B) mean = $920 and standard deviation = $8.70.
C) mean = $92 and standard deviation = $87.
D) mean = $92 and standard deviation = $870.
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E) None of These
29. There are twenty multiple-choice questions on an exam, each having responses a, b, c, or d.
Each question is worth five points and only one option per question is correct. Suppose the
student guesses the answer to each question, and the guesses from question to question are
independent. The probability that the student gets no questions correct is closest to
A) 0.00 B) 0.0032. C) 0.0243. C) 0.25. D) 0.3277. E) None of These
30. The scores on a university examination are normally distributed with a mean of
62 and a standard deviation of 11. If the bottom 5% of students will fail the
course, what is the lowest mark that a student can have and still be awarded
passing grade?
A) 62 B) 57 C) 44 D) 40 E) None of These
31. You measure the weights of a random sample of twenty-five male runners. The sample
mean is = 60 kilograms (kg). Suppose that the mean weights of male runners follow
a normal distribution with unknown mean and standard deviation s = 5 kg. You
compute a 95% confidence interval for . The 95% confidence interval for is
A) 57.936 to 62.064 B) 59.216 to 60.784 C) 58.04 to 61.96 D) 50.2 to 69.8
E) None of These
32. You measure the weights of a random sample of twenty-five male runners. The sample
mean is = 60 kilograms (kg). Suppose that the mean weights of male runners follow
a normal distribution with unknown mean and standard deviation = 5 kg. You
compute a 95% confidence interval for . The 95% confidence interval for is
A) 57.936 to 62.064 B) 59.216 to 60.784 C) 58.04 to 61.96 D) 50.2 to 69.8
E) None of These
33. To assess the accuracy of a laboratory scale, a standard weight that is known to
weigh 1 gram is repeatedly weighed a total of n times and the mean of the
weights is computed. Suppose the scale readings are normally distributed with
Unknown mean and standard deviation s = 0.01 g. How large should n be so
that a 95% confidence interval for m has a margin of error of ± 0.0001?
A) 100 B) 196 C) 10000 D) 38416 E) None of These
34. Suppose we are testing the null hypothesis H0: = 50 and the alternative
Ha:
50. A random sample of nine observations are drawn from the
population and we find the sample mean = 53 and a standard deviation,
s = 6. The P-value is closest to
A) 0.172 B) 0.086 C) 0.1336. D) 0.0668. E) None of These
35. Is the mean height for all adult American males between the ages of eighteen
and twenty-one at least 6 feet? Which of the following null and alternative
hypotheses would test this question?
A) H0: < 6 vs. Ha: > 6
B) H0: > 6 vs. Ha: < 6
C) H0: = 6 vs. Ha:
6.
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D) H0: > 6 vs. Ha:
E) None of These
<6
36. In a statistical test of hypotheses, we say the data are statistically significant at
level if
A) = 0.05.
B) is small.
C) the P-value is less than .
D) the P-value is larger than .
E) None of These
37. An SRS of 100 postal employees found that the average time these employees had worked
for the postal service was = 7 years with standard deviation s = 2 years. Assume the
distribution of the time the population of employees have worked for the postal service is
approximately normal with mean =7.5 years. Are these data evidence that has gotten
smaller ? At a 0.01 level of significance, the decisions of the hypothesis test is:
A) Fail to Reject H0 and the claim is supported
B) Fail to Reject H0 and the data does not support the claim.
C) Reject H0 and the claim is supported
D) Reject H0 and the data does not support the claim.
E) None of These
38. The water diet requires one to drink two cups of water every half hour from when
one gets up until one goes to bed, but otherwise allows one to eat whatever one
likes. Four adult volunteers agree to test the diet. They are weighed prior to
beginning the diet and after six weeks on the diet. The weights (in pounds) are
Person
1
2
3
4
Weight before the diet
180
125
240
150
Weight after six weeks
170
130
225
150
For the population of all adults, assume that the weight loss after six weeks on the diet
(weight before beginning the diet - weight after six weeks on the diet) is normally distributed.
To determine if the diet leads to weight loss,
A) we would not reject H0 at significance level 0.10.
B) we would reject H0 at significance level 0.10, but not at 0.05.
C) we would reject H0 at significance level 0.05, but not at 0.01.
D) we would reject H0 at significance level 0.01.
E) None of These
39. Which of the following is an example of a matched pairs design?
A) A teacher compares the pre-test and post-test scores of students.
B) A teacher compares the scores of students using a computer based method of
instruction with the scores of other students using a traditional method of
instruction.
C) A teacher compares the scores of students in her class on a standardized test
with the national average score.
D) None of These
40. A noted psychic was tested for ESP. The psychic was presented with 200 cards face down
and asked to determine if the card was one of five symbols: a star, cross, circle, square, or
three wavy lines. The psychic was correct in fifty cases. Let p represent the probability that the
psychic correctly identifies the symbol on the card in a random trial. Assume the 200 trials can
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be treated as an SRS from the population of all guesses the psychic would make in his lifetime.
Suppose you wished to see if there is evidence that the psychic is doing better than just guessing
(p = 0.20). At the 0.02 level of significance.
A) Fail to Reject H0 and the claim is supported
B) Fail to Reject H0 and the data does not support the claim.
C) Reject H0 and the claim is supported
D) Reject H0 and the data does not support the claim.
E) None of These
41. How large a sample n would you need to estimate p with margin of error 0.01
with 95% confidence? Use the guess p = 0.20 as the value for p.
A) n = 32
B) n = 49
C) n = 6147
D) n = 9604 E) None of These
42. How large a sample n would you need to estimate p with margin of error 0.01
with 95% confidence? No information is given about p.
A) n = 32
B) n = 49
C) n = 6147
D) n = 9604 E) None of These
Use the following to answer questions 43 - 44:
An SRS of 100 flights of a large airline (call this airline 1) showed that 64 were on time. An SRS of 100
flights of another large airline (call this airline 2) showed that 80 were on time. Let p1 and p2 be the
proportion of all flights that are on time for these two airlines.
43. A 95% confidence interval for the difference p1 - p2 is
A) - 0.2825 to - 0.0375 B) 0.0375 to 0.2825 C) None of these
44. Is there evidence of a difference in the on-time rate for the two airlines? At the
0.05 level of significance.
A) Fail to Reject H0 and the claim is supported
B) Fail to Reject H0 and the data does not support the claim.
C) Reject H0 and the claim is supported
D) Reject H0 and the data does not support the claim.
E) None of These
Use the following information for Questions 45 - 46
Tests for longevity (how long a battery lasts in continuous use) are made on two competing brands of
batteries and the results are summarized below.
BRAND X
BRAND Y
n = 14
n = 16
= 110.0
=111.4
s = 12.0
s = 15.9
45. At a 0.10 level of significance, test the claim that the variances of the two
brands of batteries are the same. The decision is
A) Fail to Reject H0, thus the claim is not supported.
B) Reject H0, thus the claim is not supported.
C) Fail to Reject H0, thus the claim is supported.
D) Reject H0, thus the claim is supported.
E) None of these
46. At a 0.10 level of significance, test the claim that the means of the two
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brands of batteries are the same. The decision is
A) Fail to Reject H0, thus the claim is not supported.
B) Reject H0, thus the claim is not supported.
C) Fail to Reject H0, thus the claim is supported.
D) Reject H0, thus the claim is supported.
E) None of these
Use the following information for Questions 47 - 48
The Chicago Police Department tests 15 cars, Chevrolet (Impala), Dodge (Intrepid) and Ford (Crown
Victoria). Each car is driven 30,000 miles and the operating costs per mile are calculated. The operating
costs, cents per mile, are:
Chevrolet
Dodge
Ford
14.0
14.2
14.6
13.8
14.6
14.5
12.9
14.0
14.8
13.6
14.5
14.5
13.7
14.2
14.1
at a 0.05 level of significance, MINITAB calculated the following analysis for an ANOVA, oneway
(unstacked).
Analysis of Variance
Source
DF
SS
Factor
2 2.338
Error
12 1.836
Total
14 4.173
Level
Chevrolet
Dodge
Ford
N
5
4
6
MS
1.169
0.153
F
7.64
P
0.007
Individual 95% CI’S For Mean
Based on Pooled StDev
Mean StDev
---------+---------+---------+--------13.600 0.418
(-------*-------)
14.325 0.275
(--------*--------)
14.450 0.259
(------*------)
---------+---------+---------+--------13.60
14.00 14.40
47. The decision about the mean operating costs of the cars is
A) Fail to Reject H0, thus the means appear to be equal.
B) Reject H0, thus the means appear to be equal.
C) Fail to Reject H0, thus at least one of the means is different
D) Reject H0, thus at least one of the means is different
E) None of These
48. Based on the operating costs per mile, the Chicago Police Department should
purchase the:
A) Chevrolet Impala, it is the best deal.
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B) Either the Dodge Intrepid or Ford Crown Victoria, they are equal on
operating costs.
C) Ford Crown Victoria, it is the best deal.
D) Dodge Intrepid, it is the best deal.
E) None of these
49. A researcher wishes to determine whether the rate of water flow (in liters per
second) over an experimental soil bed can be used to predict the amount of soil
washed away (in kilograms). In this study, the explanatory (independent)
variable is
A) amount of eroded soil. B) Rate of water flow. C) size of soil bed.
D) depth of soil bed.
E) None of These
Use the following to answer question 50.
50. The scatterplot suggests
A) There is a positive association between height and volume.
B) There is a negative association between height and volume.
C) There is a perfect positive association (r =1.0) between height and volume.
D) There is a perfect negative association (r = -1.0) between height and volume.
E) None of These
51. The coefficient of correlation measures
A) Whether there is a relation between two variables.
B) Whether or not a scatterplot shows an interesting pattern.
C) Whether a cause and effect relation exists between two variables.
D) The strength of a straight line relation between two variables.
E) None of These
Use the following to answer question 52:
Consider the following scatterplot.
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52. A plausible value for the correlation between weight and MPG is
A) +0.2 B) -0.9 C) +0.7 D) -1.0 E) None of These
53. The coefficient of correlation correlation between the age and height of children is found to
be about r = 0.7. Suppose we use the age x of a child to predict the height y of the child.
We conclude
A) The least squares regression line of y on x would have a slope of 0.7.
B) The fraction of the variation in heights explained by the least squares
regression line of y on x is 0.49.
C) About 70% of the time, age will accurately predict height.
D) Height is generally 70% of a child's age.
E) None of These
54. A study of elementary school children, ages 6 to 11, finds a high positive
correlation between shoe size x and score y on a test of reading comprehension.
The observed correlation is most likely due to
A) The effect of a lurking variable, such as age.
B) A mistake, since the correlation must be negative.
C) Cause and effect (larger shoe size causes higher reading comprehension).
D) "Reverse" cause and effect (higher reading comprehension causes larger
shoe size).
E) None of These
Use the following information for Questions 55 - 57
A Company feels that absenteeism is linearly correlated to the worker's age. The following table
summarizes the days lost at work (absenteeism) and the age of the employee. Test this claim at a 0.05 level
of significance.
AGE
19
21
28
42
52
54
ABSENTEEISM 13
9
10
9
6
2
Using MINITAB, "Absenteeism" is stored in C1 and "Age" is stored in C2. Testing for a linear correlation
and using 30 as a basis for the confidence intervals, the MINITAB analysis is
The regression equation is C1= 15.7 - 0.209 C2
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Predictor
Coef
Stdev t-ratio
P
Constant
15.704
2.406
6.53 0.003
C2
-0.20938
0.0622
-3.37 0.028
s = 2.150
R-sq = 73.9% R-sq(adj) = 67.4%
FIT STDEV.FIT
9.423
0.954
95% C.I.
95% P.I
( 6.774, 12.072 ) ( 2.891, 15.955 )
55. The decision is:
A) Fail to Reject H0 and there appears to be NO linear correlation.
B) Reject H0 and there appears to be NO linear correlation.
C) Fail to Reject H0 and there appears to be a linear correlation.
D) Reject H0 and there appears to be a linear correlation.
E) None of these.
56. The linear correlation coefficient is:
A) -0.860 B) -0.739 C) 0.739 D) 0.860
E) none of these.
57. For an individual employee, 30 years old, the 95% confidence interval for
absenteeism (days of worked missed) is:
A) Cannot be determined, there is no linear correlation.
B) ( 6.774, 12.072 )
C) ( 2.891, 15.955 )
D) 9.423
E) none of these
Use the following information for Question 58.
A random sample of 930 Chicago viewers were asked if they watched the 10 P.M. news on Channel 2,
Channel 5, or Channel 7. The results were:
Channel 2
Viewers
Channel 5
280
337
Channel 7
313
At a 0.05 level of significance, test the claim that the proportion of viewer is the same (uniform) for
each station.
58. MINITAB produced a TEST STATISTIC of 5.28387. The decision is:
A) Fail to Reject H0 and the proportions are different.
B) Reject H0 and the proportions are different.
C) Fail to Reject H0 and the proportions are equal.
D) Reject H0 and the proportions are equal.
E) None of these
Answer Key -- 212 review
1. C
2. A
3. A
10. C
11. C
12. B
19. C
20. D
21. A
28. A
29. B
30. C
37. C
38. A
39. A
46. C
47. D
48. A
4. D
13. B
22. B
31. A
40. B
49. B
5. B
14. A
23. C
32. C
41. C
50. A
6. D
15. C
24. A
33. D
42. D
51. D
7. B
16. B
25. A
34. B
43. A
52. B
8. A
17. C
26. D
35. B
44. C
53. B
9. C
18. C
27. D
36. C
45. C
54. A
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55. D
56. A
57. C
58. C
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