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Try the following 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 his or
her 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) 35% 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) 47.25 B) 48 C) 48.5 D) 49.75 E) None of These
5. The median salary for this year is
A) 47.25 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. The household income in a certain community is normally distributed with a mean of
$42,000 and a standard deviation of $5,000. The proportion of households with
incomes exceeding $38,000 is
A) 0.7881 B) 0.2119 C) 0.7119 D) 0.2881 E) None of These
8. Birth weights at a local hospital have a normal distribution with a mean of 110 oz. and
a standard deviation of 15 oz. The proportion of infants with birth weights between 125
oz. and 140 oz. is
A) 0.819 B) 0.636 C) 0.477 D) 0.136 E) None of These
9. 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
10. The time to complete a standardized exam is approximately normal with a mean of
70 minutes and a standard deviation of 10 minutes. Suppose the students are given
one hour to complete the exam. The proportion of students who don't complete the
exam is
A) 0.500 B) 0.159 C) 0.341 D) 0.841. E) None of These
11. 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 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 12.
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12. The scatterplot suggests
A) There is a positive association between height and volume.
B) There is an outlier in the plot.
C) Both a and b.
D) Neither a nor b.
E) None of These
13. 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
14. Consider the following scatterplot.
A plausible value for the coefficient of correlation between weight and MPG is
A) +0.2 B) -0.9 C) +0.7 D) -1.0. E) None of These
Use the following to answer question 15:
Consider the following scatter diagram of amounts of CO (carbon monoxide) and NOX (nitrogen oxide)
in grams per mile driven in the exhausts of cars. The least squares regression line has been drawn in the
plot.
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15. Based on the scatter diagram, the least squares line would predict that a car that
emits 10 grams of CO per mile driven would emit how many grams of NOX per mile
driven?
A) 10.0 B) 1.7 C) 2.2 D) 1.1 E) None of These
16. The 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
17. 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
18. I toss a penny and observe 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 19 - 21:
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
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19. 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
20. 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
21. 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 22 - 23:
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.
Value of x
1
2
3
4
5
6
Probability
1/6
1/6
1/6
1/6
1/6
1/6
22. 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
23. P(x < 2) has value:
A) 1/6 B) 1/3 C) 1/2
D) 2/3
E) None of These
24. A phone-in poll conducted by a newspaper reported that 73% of those who called in
liked business tycoon Donald Trump. The unknown true percentage of American
citizens who like Donald Trump is a
A) statistic. B) sample. C) parameter. D) population. E) None of These
25. 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 26:
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.
26. 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
27. 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 less than 8 oz. is
A) 0.0125. B) 0.1853. C) 0.4871. D) 0.9873. E) None of These
28. The central limit theorem says that when a simple sample of size n is drawn from any
population with mean and standard deviation , then when n is sufficiently large
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/n.
A) the standard deviation of the sample mean is
B) the distribution of the population is exactly normal.
C) the distribution of the sample mean is approximately normal.
D) the distribution of the sample mean is exactly normal.
E) None of These
29. The law of large numbers states that, as the number of observations drawn at random
from a population with finite mean m increases, the mean J of the observed values
A) gets larger and larger.
B) gets smaller and smaller.
C) gets closer and closer to the population mean m.
D) fluctuates steadily between one standard deviation above and one standard
deviation below the mean.
E) None of These
Use the following to answer question 30:
Let the random variable, x, represent the profit made on a randomly selected day by a certain store.
Assume x is normal with a mean of $360 and standard deviation $50.
30. The value of P(x > $400) is
A) 0.2881. B) 0.8450. C) 0.7881. D) 0.2119. E) None of These
31. In a large population of adults, the mean IQ is 112 with a standard deviation of 20.
Suppose 200 adults are randomly selected for a market research campaign. The
probability that the sample mean IQ is greater than 110 is
A) 0.079. B) 0.421. C) 0.921. D) 0.579. E) None of These
32. 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. The probability that the average,
, of the 100 claims is larger than $1000 is
A) 0.9200. B) 0.8212. C) 0.0800. D) 0.1788.
E) None of These
33. 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. 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.
E) None of These
34. 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
35. 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
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36. 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. 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
37. 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) 0.0032. B) 0.0243. C) 0.2373. D) 0.3277. E) None of These
38. 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
39. 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
40. 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
41. Suppose we are testing the null hypothesis H0: m = 50 and the alternative
Ha: m 50 for a normal population with s = 6. A random sample of nine observations
are drawn from the population and we find the sample mean of these observations is
= 53. The P-value is
A) 0.0668. B) 0.086
C) 0.1336.
D) 0.1720.
E) None of These
42. Is the mean height for all adult American males between the ages of eighteen and
twenty-one now over 6 feet? Given that the population of all adult American males
between the ages of eighteen and twenty-one has mean height of m feet and standard
deviation s feet, which of the following null and alternative hypotheses would one test
to answer this question?
A) H0: m < 6 vs. Ha: m > 6
B) H0: m > 6 vs. Ha: m < 6
C) H0: m = 6 vs. Ha: m 6.
D) H0: m > 6 vs. Ha: m < 6
E) None of These
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43. 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
Use the following to answer questions 44 - 45
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 changed ? At a 0.01 level of significance,
44. The decision 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
45. A 95% confidence interval for the mean time the population of postal service
employees have spent with the postal service is
A) 6.608 to 7.392.
B) 7.108 to 7.892
C) 6.6032 to 7.3968 D) 7.1032 to 7.8968.
E) None of These
46. 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 and still
lose weight. 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
215
152
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. Based on these data we conclude that
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
47. 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) A teacher calculates the average of scores of students on a pair of tests and wishes
to see if this average is larger than 80%.
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E) None of These
Use the following information for problems 48 - 49.
Researchers compared two groups of competitive rowers—a group of skilled rowers and a group of
novices. The researchers measured the angular velocity of each subject's right knee, which describes the
rate at which the knee joint opens as the legs push the body back on the sliding seat. The sample sizes,
the sample means, and the sample standard deviations for the two groups are given below.
Group
n
Mean
Standard
deviation
Skilled
16
4.2
0.6
Novice
16
3.7
0.8
48. The researchers wished to test the the claim that the mean knee velocity for skilled
rowers is larger than for novice rowers. Should the data be pooled? Use a 0.01
level of significance.
A) Fail to Reject H0 and do not pool the data
B) Fail to Reject H0 and pool the data.
C) Reject H0 and pool the data
D) Reject H0 and do not pool the data.
E) None of These
49. Use a 0.01 level of significance to test the claim that the mean knee velocity for
skilled rowers is larger than for novice rowers.
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 to answer questions 50 - 51:
A researcher wished to test the effect of the addition of extra calcium to yogurt on the "tastiness" of
yogurt. A collection of 200 adult volunteers was randomly divided into two groups of 100 subjects each.
Group 1 tasted yogurt containing the extra calcium. Group 2 tasted yogurt from the same batch as group
1 but without the added calcium. Both groups rated the flavor on a scale of 1 to 10, 1 being "very
unpleasant" and 10 being "very pleasant." The mean rating for group 1 was
1 = 6.5 with a standard
deviation s1 = 1.5. The mean rating for group 2 was 2 = 7.0 with a standard deviation s2 = 2.0.
Assume the two groups are independent. Let 1 and 2 represent the mean ratings we would observe
for the entire population represented by the volunteers if all members of this population tasted,
respectively, the yogurt with and without the added calcium.
50. A 90% confidence interval for 1
2 is
A) 0.9112 to 0.0888 B) 0.0888 to 0.9112 C) 0.7814 to 0.2186
D) 0.2186 to 0.7814
E) None of These
51. At a 0.05 level of significance, test that claim that the yogurt with Calcium tastes the
same as the yogurt without Calcium.
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.
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E) None of These
52. 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 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
53. 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
54. 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 55 - 56:
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.
55. 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
56. 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
Answer Key -- 139 review
1. C
2. B
3. A
10. D
11. B
12. C
19. A
20. C
21. C
28. C
29. C
30. D
37. A
38. A
39. C
46. A
47. A
48. B
55. A
56. C
4. D
13. D
22. C
31. C
40. D
49. B
5. B
14. B
23. B
32. D
41. B
50. A
6. D
15. D
24. C
33.A
42. A
51. D
7. A
16. B
25. A
34. A
43. C
52. B
8. D
17. A
26. A
35. C
44. B
53. C
9. C
18. B
27. A
36. B
45. A
54. D
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The content, views, and opinions on this page are strictly those of the author.
The contents of this page have not been reviewed or approved by Moraine Valley Community College.
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