Download 4309 ∑ 4919 - Bakersfield College

Math 22
Final Exam Practice
Please note that the final exam will not be in this format. This is the only way I can give you
this amount of study material and the answers to go with it. The final exam itself will be
similar to all the other exams we have taken in the class.
Kevin and Tyler bowl at the Bedrock Rock ‘n’ Bowl Lanes. Their scores are below in two stemand-leaf displays.
Kevin
Tyler
14 0
14 8 9
15 0 1 2 9
15 0
16 1 2 5 5 9
16 1
17 5 6 6 7 8 9
17 2 7
18 2 2 3 6
18 3 6 9
19 2 3 9
19 0 1 1 4
20 0
20 2 3 4 5 5
21 1 1 2 6
22 2 3
23 1
24
25 0
Calculator check: ∑ x = 4309
Calculator check: ∑ x = 4919
1. What is the basic shape of the two distributions?
a. bell shaped b. skewed c. J-shaped
d. they are different shapes
e. none of these
2. What is the range for Kevin’s bowling scores?
a. 22.5 b. 52
c. 200 d. −8 e. none of these
3. What is the interquartile range for Tyler’s bowling scores?
a. 110 b. 22.2 c. 211.5 d. 27 e. none of these
4. Report the best measure of center for Kevin’s bowling scores.
a. x = 172.36 b. M = 176 c. the mode = 176 d. x = 176 e. none of these
5. Report the best measure of center for Tyler’s bowling scores.
a. x = 196.76 b. M = 202 c. the mode = 205 d. x = 202 e. none of these
6. Which bowler has the highest standard deviation?
a. Kevin b. Tyler
7. What is the variance for Kevin’s bowling scores?
a. 247.74 b. 237.83 c. 15.74
d. 15.42 e. none of these
8. Who is the more consistent bowler?
a. Kevin b. Tyler
9. What percentage of Kevin’s scores are between 148 and 160?
a. 50% b. 75% c. 5% d. 25% e. none of these
10. Construct a 95% confidence interval for Tyler’s true median bowling score.
a. 196.76 b. (186.52, 207.00) c. (189.00, 205.00) d. (8, 17)
e. none of these
11. Construct a 95% confidence interval for Kevin’s true mean bowling score.
a. 196.76 b. (165.86, 178.86) c. (186.52, 207.00) d. (187.04, 206.48)
e. none of these
12. What is the margin of error for Kevin’s 95% confidence interval?
a. 3% b. 6.5 c. 13 d. 23 e. none of these
Both boys agree that Tyler is a better bowler - but Kevin would like to know if it is statistically
significant. Do a hypothesis test to find out if Tyler’s mean bowling score is significantly higher
than Kevin’s. Test at the 5% level of significance.
13. The bowling scores are
a. independent b. dependent
14. Check Assumptions:
a. The sample sizes are larger than 20 so by the CLT the normality assumption is
satisfied.
b. It is reasonable to assume the two samples were drawn from normal
populations because the normal plots do not show serious deviations from
normality and because of the shapes of the stem and leaf displays.
c. Successes and failures for each bowler are both at least five.
d. Normality is not needed for a t-test.
e. none of these
15. Hypothesis:
H : π − πT = 0
H : µ − µT = 0
H : µ − µT = 0
H : χ − χT = 0
a. 0 K
b. 0 K
c. 0 K
d. 0 K
H A :π K − πT > 0
H A : µ K − µT < 0
H A : µ K − µT ≠ 0
H A : χ K − χT < 0
16. α = a. 0.01 b. 0.05 c. 0.1 d. a fish e. none of these
17. Should we pool?
a. no b. yes
18. Test Statistic:
a. t = −4.1525 b. z = −4.1525 c. t = 4.1525 d. none of these
19. p-Value
a. 6.7043 b. 1.3408 c. 0.0001 d. 0.00007 e. none of these
20. Decision:
a. reject the null hypothesis b. reject the research hypothesis
c. reject Tyler bowling better than Kevin d. fail to reject the null hypothesis
21. Conclusion:
a. We can conclude that Tyler’s mean bowling score is significantly higher than
Kevin’s.
b. We cannot conclude that Tyler’s mean bowling score is significantly higher than
Kevin’s.
c. We can conclude that Rudolph the red-nosed reindeer must have kept score.
d. none of these.
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22. The number of calories in a fast food sandwich is a
(a) quantitative variable
(b) qualitative variable
23. Marital status is a
(a) quantitative variable
(b) qualitative variable
24. In order to determine the mean weight of bags of chips filled by its packing machines, a
company inspects 50 bags per day and weighs them. In this example, the population is
A) the 50 bags inspected each day.
B)all potato chips produced by the company.
C) all bags of potato chips produced by the company. D) the weight of the 50 bags inspected.
25. Which of the following sampling techniques is most likely to produce biased results?
A) systematic random sampling.
C) stratified random sample.
B) simple random sample.
D) convenience sample.
26. Below are listed the ages (in months) of children at a home day care. Choose the correct
stem and leaf display of the data. 18, 24, 25, 35, 37, 42, 47, 48, 48, 58
27. Below are the ages of 15 students in a college class. Find the standard deviation of the ages.
27, 50, 33, 25, 86, 25, 85, 31, 37, 44, 20, 36, 59, 34, 28
A) 34 B) 31 C) 41.3 D) 20.6
28. Below are the ages of 15 students in a college class. Find the variance of the ages.
27, 50, 33, 25, 86, 25, 85, 31, 37, 44, 20, 36, 59, 34, 28
A) 1156 B) 961 C) 1705.69 D) 424.7
29. Below are the lengths (in minutes) of phone calls made on an 800 line to a business on one
day. Find the five-number summary for this data.
14, 6, 12, 19, 2, 35, 5, 4, 3, 7, 5, 8
A) 5, 8, 14, 15.5, 20 B) 2, 4, 7, 14, 35 C) 2, 4, 6, 12, 19 D) 2, 4.5, 6.5, 13, 35
30. Probability – A value between 0 and 1 inclusive, that measures the likelihood that a
particular event will occur. (a) TRUE (b) FALSE
31. If events A and B are mutually exclusive, then P(A and B) = 1.
(a) TRUE (b) FALSE
32. Let P(A) = 0.35 and P(B) = 0.15 and P(A and B) = 0.05. What is the P(A or B).
(a) 0.50
(b) 0.45
(c) 0 (d) cannot be determined
(e) none of these
33. Two fair dice are rolled and the sum rolled is recorded. Find the probability that the sum is
4.
(a) 1/3 (b) 1/12 (c) 4/11 (d) 1/9 (e) none of these
34. If there is a 0.8 probability of rain today, what is the probability it will not rain?
(a) 0.8 (b) 0.5 (c) 0.2 (d) 0.1 (e) none of these
35. A sample space contains three outcomes, A, B, and C. Which of the following could be a
legitimate assignment of probabilities to the outcomes?
(a) P(A) = 0.2 P(B) = 0.4 P(C) = 0.6
(b) P(A) = 0.2 P(B) = 0.2 P(C) = 0.6
(c) P(A) = 2 P(B) = 3 P(C) = 1
(d) P(A) = 0.3 P(B) = 0.3 P(C) = 0.3
(e) none of these
36. A fair die is rolled. If a number 1 or 2 appears, you will receive $5. If any other number
appears, you will pay $2. What is the mean value of one trial of this game?
(a) $1/3 (b) $3 (c) $3/2 (d) –$3 (e) none of these
37. A fair die is rolled. If a number 1 or 2 appears, you will receive $5. If any other number
appears, you will pay $2. What is the standard deviation of one trial of this game?
(a) $3.30 (b) $10.89 (c) $11 (d) –$2 (e) none of these
38. Which of the following is not required for a binomial distribution?
(a) only 2 outcomes
(b) at least 50 observations
(c) independent trials
(d) a constant probability of success
39. If a binomial distribution has n = 10 and π = 0.4 , then P(X < 2) =
(a) 0.1209
(b) 0.4
(c) 0.8327
(d) 0.1673
(e) none of these
40. If a binomial distribution has n = 10 and π = 0.4 , then P(X > 2) =
(a) 0.1209
(b) 0.4
(c) 0.8327
(d) 0.1673
(e) none of these
41. Suppose 90% of Toro lawn mowers will start on the first pull. Eight Toro mowers are
chosen and tried once. Find the following probability: P(At least six will start).
(a) 0.1488 (b) 0.1869 (c) 0.8131 (d) 0.9619
42. A normal distribution has a mean of 30 and standard deviation of 5. Compute the z-score
when x = 37.
(a) z = 1.4
(b) z = 31 (c) z = 37 (d) z = 5 (e) none of these
43. The shelf life of a battery produced by one major company is known to be normally
distributed, with a mean life of 3.5 years and a standard deviation of 0.75 years. What is the
upper quartile of battery shelf life?
A) 4.0059 years B) 4.25 years C) 4.17 years D) 2.9941 years (e) none of these
44. The mean length of time, per week, that students at a certain school spend on their
homework is 24.3 hours, with a standard deviation of 1.4 hours. Assuming the distribution
of study times is normal, what percent of students spend more than 25 hours per week on
homework? A) 69.15% B) 5% C) 12.5% D) 30.85% (e) none of these
45. The annual income of residents in a county is $42,000 with a standard deviation of $10,000.
Assuming that the distribution of incomes is normal, between what two values do
approximately 95% of the incomes of county residents lie?
A) $40,000 and $44,000
C) $32,000 and $52,000
B) $22,000 and $62,000
D) $30,000 and $50,000
(e) none of these
46. The mean length of time, per week, that students at a certain school spend on their
homework is 24.3 hours, with a standard deviation of 1.4 hours. Assuming the distribution
of study times is normal, what percent of students study between 22.9 and 25.7 hours?
A) 99.73% B) 95.45% C) 68.27% D) 50% E) none of these
47. The weight of potato chip bags filled by a machine at a packaging plant is normally
distributed, with a mean of 15.0 ounces and a standard deviation of 0.2 ounces. What is the
probability that a randomly chosen bag will weigh more than 15.6 ounces?
A) 5% B) 2.5% C) 0.3% D) 0.13% E) none of these
A certain population has a mean of 500 and a standard deviation of 30. Many samples of size 36
are randomly selected and their mean calculated.
48. What shape would you expect the distribution of all these sample means to have?
(a) skewed (b) bimodal (c) skewered
(d) normal (e) none of these
49. What value would you expect to find for the mean of all these sample means? µ x =
(a) 500 (b) 30 (c) 5 (d) 7 (e) none of these
50. What value would you expect to find for the standard deviation of all these sample means?
σx =
(a) 500 (b) 30 (c) 5 (d) 7 (e) none of these
51. A poll of 1200 randomly selected residents in a state found that 63% favored higher taxes to
support education. Find a 95% confidence interval for the proportion of the state's residents
who support taxes for education.
A) 62.76 to 63.24% B) 62.51 to 63.49% C) 61.6 to 64.4% D) 60.3 to 65.7%
52. A random sample of 1540 adults were asked if they jog. Fifteen percent answered "yes."
Find a 95% confidence interval for the percent of all adults who would answer "yes" when
asked if they jog.
A) 14.09 to 15.91% B) 13.2 to 16.8% C) 14.79 to 15.21% D) 14.58 to 15.42%
53. This morning you weighed yourself ten times and got the following results: 146.5 lbs, 149
lbs, 148.5 lbs, 150 lbs, 145 lbs, 145.5 lbs, 151.5 lbs, 150 lbs, 148 lbs, and 147.5 lbs. Find a
95% confidence interval for your true weight. Assume normality.
A) 146.66 to 149.64 lbs B) 147.8 to 149.2 lbs C) 148.25 to 148.75 lbs D) 148 to 149
lbs
54. TRUE / FALSE. Definition: Null Hypothesis: A claim about the value of the population
parameter that is believed to be true.
55. TRUE / FALSE. Definition: Alternative Hypothesis: A claim about the population
parameter that is accepted if the null hypothesis is rejected.
56. TRUE / FALSE. Statistical hypothesis testing can never truly prove anything. The best it
can do is suggest one hypothesis is more likely than the other.
58. When considering whether to jump from an airplane, which is more serious, a Type I error or
a Type II error?
a. Type I error
H 0 : The parachute will open.
b. Type II error
H A : The parachute will not open.
c. Neither are serious.
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The following information is available:
H 0 : µ = 50
H A : µ ≠ 50
The sample mean is 49, the sample standard deviation is 5, and the sample size is 36. Use the
0.05 level of significance.
59. α = _____ : a. 0.1 b. 0.05 c. 0.5 d. none of these
60. test statistic: a. t = 1.20 b. t = −1.20 c. z = 1.20 d. z = −1.20 e. none of these
61. p-value:
a. 0.2301 b. 0.2382 c. 0.7699 d. none of these
62. Decision: a. reject H 0 b. reject H A c. fail to reject H 0 d. fail to reject H A
63. Conclusion: a. We can conclude that the mean is different than 50.
b. We can not conclude that the mean is different than 50.
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A random sample of size n = 200 resulted in x = 174 successes. Test the following at the 0.01
significance level.
H 0 : π = 0.80
H A : π > 0.80
64. α = _____ : a. 0.1 b. 0.05 c. 0.5 d. none of these
65. test statistic: a. t = 2.4749 b. t = −2.4749 c. z = 2.4749 d. z = −2.4749
66. p-value:
a. 0.0067 b. 0.05 c. 0.8700 d. none of these
67. Decision: a. reject H 0 b. reject H A c. fail to reject H 0 d. fail to reject H A
68. Conclusion: a. We can conclude that the proportion is greater than 80%.
b. We can not conclude that the proportion is greater than 80%.
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It is believed that a professional preparation service for the SAT exams will increase your score.
Ten students were chosen randomly, five had taken a preparation class and five had not. Is there
evidence that the preparation courses increase SAT score?
Preparation Class
No Preparation Class
1130
1040
1470
1240
1230
1270
630
1020
1030
1350
69.
These samples are
a) independent
b) dependent
70.
Choose the appropriate hypotheses.
H 0 : µ1 − µ2 = 0
H 0 : θ1 − θ 2 = 0
H 0 : µd = 0
H0 : θd = 0
b)
c)
d)
a)
H a : µ1 − µ 2 > 0
H a : θ1 − θ 2 > 0
H a : µd > 0
H a : θd > 0
71.
test statistic:
a) t = -0.5633
b) t = -0.5
c) t = -0.7267
d) M = -40
72.
p-value:
a)
0.7027
b) 0.6847
c) 0.7462
d) 0.8125
73.
Decision:
a. reject H 0 b. reject H A c. fail to reject H 0 d. fail to reject H A
74.
Conclusion:
a) We can conclude that the preparation courses increase SAT score.
b) We cannot conclude that preparation courses increase SAT score.
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Many believe that males are more in favor of the death penalty than females. In a particular state,
a poll was taken in which respondents were asked whether they were in favor of the death
penalty. Of the 217 women surveyed, 199 were in favor of the death penalty. Of the 211 men
surveyed, 201 were in favor. Do the results of the survey support the idea that men are more in
favor of the death penalty than women? Let sample 1 = women and sample 2 = men.
75.
Choose the appropriate hypotheses:
H 0 : µ1 − µ2 = 0
H 0 : π1 − π 2 = 0
H 0 : π1 − π 2 = 0
H 0 : µ1 − µ2 = 0
a)
b)
c)
d)
H a : µ1 − µ 2 > 0
H a : π1 − π 2 > 0
H a : π1 − π 2 < 0
H a : µ1 − µ 2 < 0
76.
test statistic:
a) z = -1.4873
b) z = 1.4873
c) t = -1.5130
d) t = 1.5130
77.
p-value:
a) 0.0655
b) 0.0685
c) 0+
d) 1
78.
Conclusion:
a) We can conclude that males are more in favor of the death penalty than women.
b) We cannot conclude that males are more in favor of the death penalty than women.
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Some students take the SAT test more than once to improve their score. Below are scores for
eight students that took the exam more than once. Is there statistical evidence that repeating the
test will improve the test score?
Student 1
2
3
4
5
6
7
8
840
1290
1260
800
920
1240
1260
740
1st test
nd
1240
1270
1030
1130
1470
1230
630
2 test 1040
79.
These samples are
a) independent
b) dependent
80.
Choose the appropriate hypotheses:
H 0 : µ1 − µ2 = 0
H 0 : θ1 − θ 2 = 0
H 0 : µd = 0
H0 : θd = 0
a)
b)
c)
d)
H a : µd > 0
H a : θd > 0
H a : µ1 − µ 2 > 0
H a : θ1 − θ 2 > 0
81.
p-value:
a) 0.3633
b) 0.0675
c) 0.2447
d) 0.3631
82.
Decision:
a. reject H 0 b. reject H A c. fail to reject H 0 d. fail to reject H A
83.
Conclusion:
a) We can conclude that taking the test a second time increases the score.
b) We cannot conclude that taking the test a second time increases the score.
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84. If the chi-square test is to be applied to data cross-classified in a contingency table,
(a) the expected frequencies cannot be determined
(b) the observed frequencies must total 100
(c) there must be at least 10 expected frequencies in each cell
(d) a black cat must not be in the room when you do your calculations
(e) none of these
85. The chi-square distribution
(a) is skewed (b) never assumes a negative value (c) all of the above
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A manufacturer of women’s apparel wants to know if a women’s age is a factor in determining
whether she will buy a particular garment. Accordingly, the firm surveyed three age groups and
asked each woman to rate the garment as excellent, average, or poor. The results follow. Test
the hypothesis, at the 0.05 level, that rating is not related to age group.
15 to 25
25 to 40
40 to 55
Total
Excellent
40
47
46
133
Average
51
74
57
182
Poor
29
19
37
85
Total
120
140
140
400
86. Find the expected count for Excellent and age 15 to 25.
a. 46.55 b. 40 c. 39.9 d. 133
e. none of these
87. Hypothesis:
a. H 0 : The Rating of the clothing is independent of (not related to ) age group.
H A : The Rating of the clothing is dependent of ( related to ) age group.
b. H 0 : The Rating of the clothing is dependent of ( related to ) age group.
H A : The Rating of the clothing is independent of (not related to ) age group.
88. Test Statistic: a. t = 8.7503 b. z = 8.3 c. χ 2 = 8.7503
89. p-Value: a. 0.05 b. 0.0677 c. 1 d. 0
90. Decision: a. Reject H 0
b. fail to Reject H 0
*****************************************************************************
Students are given three different choices for ordering textbooks for classes: online, by mail, or
in the bookstore. The manager of the college bookstore says that 70% of textbooks are
purchased in the bookstore, while the remaining 30% are evenly divided between online and mail
orders. Does the following data indicate that the distribution is different from what the manager
believes?
Bookstore
Online
Mail
Observed
267
60
48
Expected
91.
Choose the appropriate null hypothesis:
a)
Ho: π1 = 0.70 π2 = 0.30 π3 = 0.30
b)
Ho: π1 ≠ 0.70 π2 ≠ 0.30 π3 ? 0.30
c)
Ho: π1 = 0.70 π2 = 0.15 π3 = 0.15
d)
Ho: π1 ≠ 0.70 π2 ? 0.15 π3 ≠ 0.15
92.
What is the expected count for online orders?
a) 56.25
b) 112.5
c) 262.5
d) 60
c) χ2 = 1.5371
d) χ2 = 139,879.7541
93.
test statistic:a) χ2 = -1.5371 b) χ2 = 0
94.
p-value:a) 0+
b) 1.0
c) 0.4637
d) -1.0
95.
Conclusion:
a) We can conclude that the distribution is different from what the manager suggests.
b) We cannot conclude that the distribution is different from what the manager suggests.
Below are data on the age of ten cars and the amount spent on auto repairs in one year.
age (years)
2
3
3
5
6
7
10 12 12 15
x
auto repairs ($)
120 175 160 250 325 380 500 615 630 770
y
96. Make a scatter plot of the data. What is the trend in the data?
(a) There is a negative linear trend in the data.
(b) There is a positive linear trend in the data.
(c) There is no trend in the data.
(d) There is a monotonic shape to the data.
(e) none of these
97. Calculate the appropriate correlation coefficient.
(a) r = 0.9976 (b) r = 0.9988 (c) rs = 0.9939 (d) rs = −0.9988
(e) none of these
98. Report the regression equation.
(a) y = 50.1781x + 16.1644
(b) y = 16.1644x + 50.1781
(c) y = 0.0199x − 0.3033
(d) none of these
99. Della is buying an 11 year old car - predict how much she will spend in auto repairs the first
year.
(a) $227.99
(b) $568.12
(c) $−0.08
(d) none of these
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The quanitity of oxygen dissolved in water is a measure of water pollution. Samples are taken at
4 locations in a lake, and the quantities of dissolved oxygen appear below. (lower readings
indicate greater pollution).
Location
Quantity
(1)Tyler Creek
6.5 6.4 6.9 7.1
(2)Kevin Cove
6.7 7.1 6.9 7.3 7.2
(3)Katie Bluffs
7.4 6.9 7.2
(4)Doug Beach
6.5 6.4 6.9 7.2
Do these data indicate significant differences in the mean amounts of dissolved oxygen at the 4
locations? Assume that samples are independently drawn from normal populations.
100. Hypothesis:
H 0: µ1 = µ 2 = µ 3
H 0: µ1 = µ 2 = µ 3 = µ 4
(a)
(b)
H A : at least two means differ
H A : at least two means differ
(c)
H 0 : θ1 = θ 2 = θ 3
H A : θ1 ≠ θ 2 ≠ θ 3
101. Test Statistic:
(a) F = 1.9024 (b) F = 2.4954 (c) H = 1.9024 (d) none of these
102. p-Value:
(a) 0.8803 (b) 0.1373 (c) 0.1831 (d) none of these
103. Decision:
(a) Reject H 0 (b) fail to Reject H 0
Math 22, Final Review Practice Answers
1. a
2. b
3. d
4. a
5. a
11. b
12.b
13. a
14. b
15. b
21. a
22. a
23. b
24. c
25. d
31. b
32. b
33. b
34. c
35. b
41. d
42. a
43. a
44. d
45. b
51. d
52. b
53. a
54. T
55. T
61. b
62. c
63. b
64. d
65. c
71. b
72. b
73. c
74. b
75. c
81. a
82. c
83. b
84. e
85. c
91. c
92. a
93. c
94. c
95. b
101. a 102. c 103. b
6. b
16. b
26. b
36. a
46. c
56. T
66. a
76. a
86. c
96. b
7. a
17. b
27. d
37. a
47. d
57.
67. a
77. b
87. a
97. b
8. a
18. a
28. d
38. b
48. d
58. b
68. a
78. b
88. c
98. a
9. d
19. d
29. d
39. d
49. a
59. b
69. a
79. b
89. b
99. b
10. c
20. a
30. a
40. c
50. c
60. b
70. b
80. d
90. b
100. b