Midterm Exam Review Statistics Instructor: RezaKhadem
Please show all work, NWNC, no work no credit! Please keep in mind that although calculators are allowed on this test the
algebraic steps to arrive at an answer MUST be shown. Write the correct answer in the space provided for each problem.
Name: -------------------------------------------------- Days/Times: -------------------------------------Identify the population and the sample.
1) A survey of 1353 American households found that 18% of the households own a
1)
computer.
Determine whether the numerical value is a parameter or a statistic. Explain your reasoning.
2) A recent survey by the alumni of a major university indicated that the average salary of
10,000 of its 300,000 graduates was $125,000.
2)
Identify whether the statement describes inferential statistics or descriptive statistics.
3) The average age of the students in a statistics class is 22 years. Does this statement describe:
A) descriptive statistics
B) inferential statistics
Provide an appropriate response.
4) Explain the difference between a sample and a population.
Determine whether the data are qualitative or quantitative.
5) the colors of automobiles on a used car lot
A) quantitative
B) qualitative
Identify the data setʹs level of measurement.
6) hair color of women on a high school tennis team
A) nominal
B) interval
C) ordinal
3)
4)
5)
6)
D) ratio
Decide which method of data collection you would use to collect data for the study. Specify either observational
study, experiment, simulation, or survey
7) A study where a drug was given to 57 patients and a placebo to another group of 57 patients to
7)
determine if the drug has an effect on a patientʹs illness
A) survey
B) observational study
C) simulation
D) experiment
Identify the sampling technique used.
8) Thirty-five sophomores, 35 juniors and 49 seniors are randomly selected from 230 sophomores,
280 juniors and 577 seniors at a certain high school.
A) systematic
B) random
C) convenience
D) stratified
E) cluster
Provide an appropriate response.
9) Explain what bias there is in a study done entirely online.
1
9)
8)
Use the given frequency distribution to find the
(a) class width.
(b) class midpoints of the first class.
(c) class boundaries of the first class.
10)
Height (in inches)
Class Frequency, f
50 - 52
5
53 - 55
8
56 - 58
12
59 - 61
13
62 - 64
11
A) (a) 3
(b) 51
(c) 50-52
10)
B) (a) 3
(b) 51
(c) 49.5-52.5
C) (a) 2
(b) 51.5
(c) 50-52
D) (a) 2
(b) 51.5
(c) 49.5-52.5
Use the given frequency distribution to construct a frequency histogram, a relative frequency histogram and a frequency
polygon.
11)
11)
Height (in inches)
Class Frequency, f
50 - 52
5
53 - 55
8
56 - 58
12
59 - 61
13
62 - 64
11
Provide an appropriate response.
12) A city in the Pacific Northwest recorded its highest temperature at 74 degrees Fahrenheit and its
lowest temperature at 23 degrees Fahrenheit for a particular year. Use this information to find the
upper and lower limits of the first class if you wish to construct a frequency distribution with 10
classes.
A) 23-29
B) 18-28
C) 23-28
D) 23-27
13) The numbers of home runs that Sammy Sosa hit in the first 15 years of his major league
baseball career are listed below. Make a stem-and-leaf plot for this data. What can you
conclude about the data?
13)
4 15 10 8 33 25 36 40 36 66 63 50 64 49 40
14) The Highway Patrol, using radar, checked the speeds (in mph) of 30 passing motorists at a
checkpoint. The results are listed below. Construct a dot plot for the data.
44 38 41 50 36 36 43 42 49 48
35 40 37 41 43 50 45 45 39 38
50 41 47 36 35 40 42 43 48 33
2
14)
12)
For the given data , construct a frequency distribution and frequency histogram of the data using five classes. Describe
the shape of the histogram as symmetric, uniform, negatively skewed, or positively skewed.
15)
15) Data set: California Pick Three Lottery
3 6 7 6 0 6 1 7 8 4
1 5 7 5 9 1 5 3 9 9
2 2 3 0 8 8 4 0 2 4
A) uniform
C) negatively skewed
B) positively skewed
D) symmetric
Provide an appropriate response.
16) Find the mean, median, and mode of the following numbers:
16)
88 91 84 88 81 89 88 82 83 86
17) A student receives test scores of 62, 83, and 91. The studentʹs final exam score is 88 and homework
score is 76. Each test is worth 20% of the final grade, the final exam is 25% of the final grade, and
the homework grade is 15% of the final grade. What is the studentʹs mean score in the class?
A) 80.6
B) 85.6
C) 90.6
D) 76.6
Approximate the mean of the grouped data.
18)
Miles (per day) Frequency
1-2
22
3-4
30
5-6
3
7-8
28
9-10
5
A) 4
B) 18
18)
C) 5
D) 6
Provide an appropriate response.
19) For the stem-and-leaf plot below, find the range of the data set.
19)
Key: 2 7 = 27
1
2
2
3
3
4
1 5
6 6 6 7 8 9
7 7 7 8 8 9 9 9
0 1 1 2 3 4 4 5
6 6 6 7 8 8 9
0 2
A) 11
17)
B) 42
C) 33
3
D) 31
20) Without performing any calculations, use the stem-and-leaf plots to determine which statement is
accurate.
(i) 0
1
2
3
4
9
(ii) 10
5 8
11
3 3 7 7
12
2 5
13
1
14
20)
9
(iii) 0
5 8
1 5
3 3 7 7
2 3 3 3 3 7 7 7 7
2 5
3 5
1
4
A) Data set (i) has the smallest standard deviation.
B) Data set (ii) has the greatest standard deviation.
C) Data sets (i) and (ii) have the same standard deviation.
D) Data sets (i) and (iii) have the same range.
21) You need to purchase a battery for your car. There are two types available. Type A has a
mean life of five years and a standard deviation of one year. Type B has a mean life of five
years and a standard deviation of one month. Both batteries cost the same. Which one
should you purchase if you are concerned that your car will always start? Explain your
reasoning.
21)
22) Adult IQ scores have a bell-shaped distribution with a mean of 100 and a standard deviation of 15.
Use the Empirical Rule to find the percentage of adults with scores between 70 and 130.
A) 100%
B) 95%
C) 99.7%
D) 68%
23) Heights of adult women have a mean of 63.6 in. and a standard deviation of 2.5 in. Does
Chebyshevʹs Theorem say about the percentage of women with heights between 58.6 in.
and 68.6 in.?
23)
24) For the following data set, approximate the sample standard deviation.
Miles (per day) Frequency
1-2
9
3-4
22
5-6
28
7-8
15
9-10
4
A) 2.1
B) 5.1
C) 1.6
22)
24)
D) 2.9
25) In a random sample, 10 students were asked to compute the distance they travel one way
to school to the nearest tenth of a mile. The data is listed below. Compute the coefficient of
variation.
25)
1.1 5.2 3.6 5.0 4.8 1.8 2.2 5.2 1.5 0.8
26) The test scores of 30 students are listed below. Find Q3 .
31 41 45 48 52 55 56 56 63 65
67 67 69 70 70 74 75 78 79 79
80 81 83 85 85 87 90 92 95 99
A) 85
B) 31
C) 78
4
26)
D) 83
27) Find the z-score for the value 88, when the mean is 95 and the standard deviation is 7.
A) z = -1.14
B) z = -1.00
C) z = -0.85
D) z = 0.85
27)
28) The ages of 10 grooms at their first marriage are listed below. Find the midquartile.
28)
35.1 24.3 46.6 41.6 32.9 26.8 39.8 21.5 45.7 33.9
A) 43.7
B) 34.2
C) 34.5
D) 34.1
29) The cholesterol levels (in milligrams per deciliter) of 30 adults are listed below. Find D6 .
154 156 165 165 170 171 172 180 184 185
189 189 190 192 195 198 198 200 200 200
205 205 211 215 220 220 225 238 255 265
A) 205
B) 171
C) 200
D) 265
30) A coin is tossed. Find the probability that the result is heads.
A) 0.1
B) 1
C) 0.5
D) 0.9
29)
30)
31) Identify the sample space of the probability experiment: shooting a free throw in
basketball.
31)
32) Classify the statement as an example of classical probability, empirical probability, or subjective
probability. The probability that a train will be in an accident on a specific route is 1%.
A) subjective probability
B) empirical probability
C) classical probability
3
33) The P(A) = . Find the odds of winning an A.
5
A) 2:3
32)
33)
B) 5:2
C) 3:5
D) 3:2
34) Classify the events as dependent or independent. Events A and B where
P(A) = 0.7, P(B) = 0.8, and P(A and B) = 0.56
A) independent
B) dependent
34)
35) A group of students were asked if they carry a credit card. The responses are listed in the table.
35)
Class
Freshman
Sophomore
Total
Credit Card Not a Credit Card
Carrier
Carrier
Total
24
36
60
37
3
40
61
39
100
If a student is selected at random, find the probability that he or she owns a credit card given that
the student is a freshman. Round your answer to three decimal places.
A) 0.240
B) 0.400
C) 0.393
D) 0.600
36) You are dealt two cards successively without replacement from a standard deck of 52 playing
cards. Find the probability that the first card is a two and the second card is a ten. Round your
answer to three decimal places.
A) 0.500
B) 0.006
C) 0.994
D) 0.250
5
36)
37) Use Bayesʹ theorem to solve this problem. A storeowner purchases stereos from two companies.
From Company A, 250 stereos are purchased and 1% are found to be defective. From Company B,
950 stereos are purchased and 10% are found to be defective. Given that a stereo is defective, find
the probability that it came from Company A.
1
38
19
10
B)
C)
D)
A)
39
39
195
39
37)
38) Decide if the events A and B are mutually exclusive or not mutually exclusive. A die is rolled.
A: The result is an odd number.
B: The result is an even number.
A) not mutually exclusive
B) mutually exclusive
38)
39) A card is drawn from a standard deck of 52 playing cards. Find the probability that the card is an
ace or a king.
2
4
1
8
B)
C)
D)
A)
13
13
13
13
39)
40) Use the pie chart, which shows the number of Congressional Medal of Honor recipients, to
find the probability that a randomly chosen recipient served in the Army, Navy, or
Marines.
40)
41) The access code to a houseʹs security system consists of seven digits. How many different codes are
available if each digit can be repeated?
A) 1,000,000
B) 64
C) 46,656
D) 6
42) A certain code is a sequence of 6 digits. What is the probability of generating 6 digits and
getting the code consisting of 1,2,3, . . ., 6 if each digit can be repeated?
43) State whether the variable is discrete or continuous.
The number of cups of coffee sold in a cafeteria during lunch
A) discrete
B) continuous
6
41)
42)
43)
44) The random variable x represents the number of cars per household in a town of 1000 households.
Find the probability of randomly selecting a household that has less than two cars.
Cars Households
0
125
1
428
2
256
3
108
4
83
A) 0.809
B) 0.125
C) 0.428
44)
D) 0.553
45) A sports analyst records the winners of NASCAR Winston Cup races for a recent season.
The random variable x represents the races won by a driver in one season. Use the
frequency distribution to construct a probability distribution.
45)
Wins
1 2 3 4 5 6 7
Drivers 12 2 0 2 0 0 1
46) Determine whether the distribution represents a probability distribution. If not, identify
any requirements that are not satisfied.
x
1
2
3
4
5
46)
P(x)
0.2
0.2
0.2
0.2
0.2
47) The random variable x represents the number of boys in a family of three children. Assuming that
boys and girls are equally likely, find the mean and standard deviation for the random variable x.
A) mean: 1.50; standard deviation: 0.76
B) mean: 2.25; standard deviation: 0.76
C) mean: 1.50; standard deviation: 0.87
D) mean: 2.25; standard deviation: 0.87
48) Decide whether the experiment is a binomial experiment. If it is not, explain why. You
observe the gender of the next 150 babies born at a local hospital. The random variable
represents the number of girls.
48)
49) Assume that male and female births are equally likely and that the birth of any child does
not affect the probability of the gender of any other children. Suppose that 650 couples
each have a baby; find the mean and standard deviation for the number of girls in the 650
babies.
49)
50) Assume that male and female births are equally likely and that the birth of any child does not
affect the probability of the gender of any other children. Find the probability of exactly eight boys
in ten births.
A) 0.8
B) 0.044
C) 0.08
D) 0.176
51) You observe the gender of the next 100 babies born at a local hospital. You count the
number of girls born. Identify the values of n, p, and q, and list the possible values of the
random variable x.
7
51)
47)
50)
52) Find the area under the standard normal curve between z = 0 and z = 3.
A) 0.0010
B) 0.9987
C) 0.4641
D) 0.4987
53) Use the standard normal distribution to find P(0 < z < 2.25).
A) 0.8817
B) 0.7888
C) 0.5122
D) 0.4878
52)
53)
Provide an appropriate response. Use the Standard Normal Table to find the probability.
54) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. An
individualʹs IQ score is found to be 110. Find the z-score corresponding to this value.
A) 1.33
B) -1.33
C) 0.67
D) -0.67
55) The lengths of pregnancies are normally distributed with a mean of 268 days and a
standard deviation of 15 days. Out of 50 pregnancies, how many would you expect to last
less than 250 days?
Provide an appropriate response.
56) Find the z-score that corresponds to the given area under the standard normal curve.
54)
55)
56)
57) For the standard normal curve, find the z-score that corresponds to the 90th percentile.
A) 2.81
B) 1.52
C) 1.28
D) 0.28
57)
58) IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the
x-score that corresponds to a z-score of 2.33.
A) 134.95
B) 139.55
C) 125.95
D) 142.35
58)
59) The distribution of room and board expenses per year at a four -year college is normally
distributed with a mean of $5850 and standard deviation of $1125. Random samples of size 20 are
drawn from this population and the mean of each sample is determined. Which of the following
mean expenses would be considered unusual?
A) $5180
B) $6180
C) $6350
D) none of these
59)
60) The lengths of pregnancies are normally distributed with a mean of 267 days and a standard
deviation of 15 days. If 36 women are randomly selected, find the probability that they have a
mean pregnancy between 267 days and 269 days.
A) 0.2119
B) 0.2881
C) 0.5517
D) 0.7881
60)
61) A study of 800 homeowners in a certain area showed that the average value of the homes
is $182,000 and the standard deviation is $15,000. If 50 homes are for sale, find the
probability that the mean value of these homes is less than $185,000. Remember: check to
see if the finite correction factor applies.
8
61)
62) In a recent survey, 90% of the community favored building a police substation in their
neighborhood. You randomly select 16 citizens and ask each if he or she thinks the
community needs a police substation.
Decide whether you can use the normal distribution to approximate the binomial
distribution. If so, find the mean and standard deviation. If not, explain why.
62)
63) Ten percent of the population is left-handed. A class of 100 students is selected. Convert the
binomial probability P(x > 12) to a normal probability by using the correction for continuity.
A) P(x < 11.5)
B) P(x ≥ 11.5)
C) P(x ≤ 12.5)
D) P(x > 12.5)
64) The failure rate in a statistics class is 30%. In a class of 50 students, find the probability that
exactly five students will fail. Use the normal distribution to approximate the binomial
distribution.
63)
64)
65) Find the critical value z c that corresponds to a 94% confidence level.
A) ±1.88
B) ±2.33
C) ±1.96
65)
D) ±1.645
66) Determine the sampling error if the grade point averages for 10 randomly selected students from a
66)
class of 125 students has a mean of x = 2.8. Assume the grade point average of the 125 students has
a mean of
μ = 3.5.
A) 3.15
B) 2.45
C) 0.7
D) -0.7
67) A random sample of 150 students has a grade point average with a mean of 2.86 and with a
standard deviation of 0.78. Construct the confidence interval for the population mean, μ, if c =
0.98.
A) (2.71, 3.01)
B) (2.43, 3.79)
C) (2.51, 3.53)
D) (2.31, 3.88)
67)
68) The standard IQ test has a mean of 100 and a standard deviation of 13. We want to be 98% certain
that we are within 2 IQ points of the true mean. Determine the required sample size.
A) 1
B) 16
C) 230
D) 330
68)
69) There were 800 math instructors at a mathematics convention. Forty instructors were
randomly selected and given an IQ test. The scores produced a mean of 130 with a
standard deviation of 10. Find a 95% confidence interval for the mean of the 800
instructors. Use the finite population correction factor.
69)
70) Find the critical value, tc for c = 0.99 and n = 10.
A) 3.169
70)
B) 1.833
C) 2.262
71) Find the value of E, the margin of error, for c = 0.90, n = 16 and s = 2.3.
A) 1.01
B) 0.19
C) 0.77
D) 3.250
71)
D) 0.25
72) When 325 college students were surveyed,115 said they own their car. Find a point estimate for p,
the population proportion of students who own their cars.
A) 0.261
B) 0.354
C) 0.646
D) 0.548
9
72)
73) In a survey of 2480 golfers, 15% said they were left-handed. The surveyʹs margin of error was 3%.
Construct a confidence interval for the proportion of left-handed golfers.
A) (0.12, 0.18)
B) (0.11, 0.19)
C) (0.18, 0.21)
D) (0.12, 0.15)
73)
74) A researcher at a major hospital wishes to estimate the proportion of the adult population of the
United States that has high blood pressure. How large a sample is needed in order to be 99%
confident that the sample proportion will not differ from the true proportion by more than 4%?
A) 2073
B) 849
C) 17
D) 1037
74)
75) The mean age of bus drivers in Chicago is 50.9 years. Write the null and alternative
hypotheses.
75)
76) Given H0 : p ≥ 80% and Ha : p < 80%, determine whether the hypothesis test is left-tailed,
right-tailed, or two-tailed.
A) two-tailed
B) left-tailed
76)
C) right-tailed
77) The mean age of bus drivers in Chicago is 57.9 years. Identify the type I and type II errors
for the hypothesis test of this claim.
77)
78) The mean age of bus drivers in Chicago is 47.4 years. If a hypothesis test is performed, how should
you interpret a decision that rejects the null hypothesis?
A) There is sufficient evidence to support the claim μ = 47.4.
B) There is not sufficient evidence to reject the claim μ = 47.4.
C) There is sufficient evidence to reject the claim μ = 47.4.
D) There is not sufficient evidence to support the claim μ = 47.4.
78)
79) Given H0 : μ ≤ 12, for which confidence interval should you reject H0 ?
79)
A) (11.5, 12.5)
B) (13, 16)
C) (10, 13)
80) Given H0 : p = 0.85 and α = 0.10, which level of confidence should you use to test the claim?
A) 80%
B) 99%
C) 90%
81) Suppose you are using α = 0.05 to test the claim that μ > 13 using a P-value. You are given the
sample statistics n = 50, x = 13.3, and s = 1.2. Find the P-value.
A) 0.1321
B) 0.0384
C) 0.0012
80)
D) 95%
81)
D) 0.0128
82) Given H0 : μ = 25, Ha : μ ≠ 25, and P = 0.033. Do you reject or fail to reject H0 at the 0.01 level of
82)
significance?
A) reject H0
B) fail to reject H0
C) not sufficient information to decide
83) Find the critical value for a right-tailed test with α = 0.01 and n = 75.
A) 1.96
B) 2.33
C) 1.645
10
83)
D) 2.575
84) You wish to test the claim that μ > 6 at a level of significance of α = 0.05 and are given sample
84)
statistics n = 50, x = 6.3, and s = 1.2. Compute the value of the standardized test statistic. Round
your answer to two decimal places.
A) 0.98
B) 2.31
C) 3.11
D) 1.77
85) Find the critical values for a sample with n = 10 and α = 0.05 if H0 : μ ≥ 20.
A) -2.262
B) -1.383
C) -3.250
85)
D) -1.833
86) Find the standardized test statistic t for a sample with n = 12, x = 30.2, s = 2.2, and α = 0.01 if
H0 : μ = 29. Round your answer to three decimal places.
A) 2.132
B) 2.001
C) 1.890
86)
D) 1.991
87) A local group claims that the police issue more than 60 speeding tickets a day in their area.
To prove their point, they randomly select two weeks. Their research yields the number of
tickets issued for each day. The data are listed below. At α = 0.01, test the groupʹs claim
using P-values.
87)
70 48 41 68 69 55 70
57 60 83 32 60 72 58
88) Determine whether the normal sampling distribution can be used. The claim is p = 0.75 and the
sample size is n = 18.
A) Use the normal distribution.
B) Do not use the normal distribution.
88)
89) Classify the two given samples as independent or dependent.
89)
Sample 1: Pre-training weights of 19 people
Sample 2: Post-training weights of 19 people
A) independent
B) dependent
90) Find the standardized test statistic to test the claim that μ1 = μ2 . Two samples are randomly
90)
selected from each population. The sample statistics are given below.
n 1 = 50
n 2 = 60
x1 = 31
s 1 = 1.5
x2 = 29
s 2 = 1.9
A) 3.8
B) 6.2
C) 4.2
D) 8.1
91) A local bank claims that the waiting time for its customers to be served is the lowest in the
area. A competitor bank checks the waiting times at both banks. The sample statistics are
listed below. Use α = 0.05 and a confidence interval to test the local bankʹs claim.
Local Bank
n 1 = 45
Competitor Bank
n 2 = 50
x1 = 5.3 minutes
s 1 = 1.1 minutes
x2 = 5.6 minutes
s 2 = 1.0 minute
11
91)
92) Find the critical values, t0 , to test the claim that μ1 = μ2 . Two samples are randomly selected and
92)
2
come from populations that are normal. The sample statistics are given below. Assume that σ 1 ≠
2
σ 2.
Use α = 0.05.
n 1 = 25 n 2 = 30
x1 = 29
x2 = 27
s 1 = 1.5 s 2 = 1.9
A) ±1.711
B) ±2.064
C) ±2.492
D) ±2.797
93) Find the standardized test statistic, t, to test the claim that μ1 = μ2 . Two samples are randomly
93)
selected and come from populations that are normal. The sample statistics are given below.
Assume that
2
2
σ 1 ≠ σ 2 .
n 1 = 25 n 2 = 30
x1 = 27
x2 = 25
s 1 = 1.5 s 2 = 1.9
A) 3.287
B) 1.986
C) 2.892
D) 4.361
94) Construct a 90% confidence interval for μ1 - μ2 . Two samples are randomly selected from normal
94)
2
2
populations. The sample statistics are given below. Assume that σ 1 = σ 2 .
n 1 = 10 n 2 = 12
x1 = 25 x2 = 23
s 1 = 1.5 s 2 = 1.9
A) (0.721, 3.279)
B) (1.335, 3.012)
C) (1.554, 3.651)
D) (1.413, 3.124)
95)
95) Data sets A and B are dependent. Find d.
A 37 35
B
35
31
A) -5.1
54
32
50 38
42
29
B) 25.2
C) 9.0
D) 33.1
96) Construct a 95% confidence interval for data sets A and B. Data sets A and B are dependent.
Round to the nearest tenth.
A 30 28 47
B
28
24
25
A) (-0.7, 18.7)
43
35
31
22
B) (-15.3, 15.4)
C) (-0.1, 12.8)
12
D) (-1.3, 9.0)
96)
97) Find the weighted estimate, p to test the claim that p1 = p2 . Use α = 0.05. The sample statistics
97)
listed below are from independent samples.
Sample statistics: n 1 = 50, x1 = 35, and n 2 = 60, x2 = 40
A) 0.682
B) 1.367
C) 0.238
D) 0.328
98) Construct a 95% confidence interval for p1 - p2 . The sample statistics listed below are from
98)
independent samples.
Sample statistics: n 1 = 50, x1 = 35, and n 2 = 60, x2 = 40
A) (-1.341, 1.781)
B) (-0.141, 0.208)
C) (-0.871, 0.872)
D) (-2.391, 3.112)
99) Given the length of a humanʹs femur, x, and the length of a humanʹs humerus, y, would you expect
a positive correlation, a negative correlation, or no correlation?
A) negative correlation
B) positive correlation
C) no correlation
Identify the explanatory variable and the response variable.
100) An agricultural business wants to determine if the rainfall in inches can be used to predict
the yield per acre on a wheat farm.
Provide an appropriate response.
101) The data below are the gestation periods, in months, of randomly selected animals and
their corresponding life spans, in years. Construct a scatter plot for the data. Determine
whether there is a positive linear correlation, a negative linear correlation, or no linear
correlation.
Gestation, x
Life span, y
8
30
2.1
12
1.3
6
1
3
11.5
25
5.3
12
3.8
10
100)
101)
24.3
40
102)
102) Calculate the correlation coefficient, r, for the data below.
x
y
-10 -8 -1 -4 -6 -7 -5 -3 -2 -9
-12 -10 7 -1 -4 -8 -3 1 4 -10
A) 0.881
B) 0.990
C) 0.792
D) 0.819
103) Calculate the coefficient of correlation, r, letting Row 1 represent the x-values and Row 2
represent the y-values. Now calculate the coefficient of correlation, r, letting Row 2
represent the x-values and Row 1 represent the y-values. What effect does switching the
explanatory and response variables have on the correlation coefficient?
Row 1
Row 2
-8 -6 1 -2 -4 -5 -3 -1 0 -7
-18 0 1 -7 -10 -14 -9 -5 -2 0
13
99)
103)
104)
104) Find the equation of the regression line for the given data.
x
y
-5 -3 4 1 -1 -2 0 2 3 -4
-10 -8 9 1 -2 -6 -1 3 6 -8
^
^
A) y = 0.522x - 2.097
B) y = -0.552x + 2.097
^
^
C) y = 2.097x + 0.552
D) y = 2.097x - 0.552
105) Find the equation of the regression line by letting Row 1 represent the x-values and Row 2
represent the y-values. Now find the equation of the regression line letting Row 2
represent the x-values and Row 1 represent the y-values. What effect does switching the
explanatory and response variables have on the regression line?
105)
Row 1 -5 -3 4 1 -1 -2 0 2 3 -4
Row 2 -10 -8 9 1 -2 -6 -1 3 6 -8
106) The frequency distribution shows the ages for a sample of 100 employees. Find the
expected frequencies for each class to determine if the employee ages are normally
distributed.
Class boundaries
29.5 - 39.5
39.5 - 49.5
49.5 - 59.5
59.5 - 69.5
69.5 - 79.5
106)
Frequency, f
14
29
31
18
8
107) Many track runners believe that they have a better chance of winning if they start in the inside lane
that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is
Lane 2, and so on until the outermost lane, Lane 6. The data lists the number of wins for track
runners in the different starting positions. Calculate the chi-square test statistic χ 2 to test the claim
that the number of wins is uniformly distributed across the different starting positions. The results
are based on 240 wins.
Starting Position 1 2 3 4 5 6
Number of Wins 50 45 32 36 44 33
A) 12.592
B) 9.326
C) 6.750
D) 15.541
108) The frequency distribution shows the ages for a sample of 100 employees. Are the ages of
employees normally distributed? Use α = 0.05.
Class boundaries
29.5 - 39.5
39.5 - 49.5
49.5 - 59.5
59.5 - 69.5
69.5 - 79.5
Frequency, f
14
29
31
18
8
14
108)
107)
109) The contingency table below shows the results of a random sample of 400 state representatives that
was conducted to see whether their opinions on a bill are related to their party affiliation.
109)
Opinion
Party
Approve Disapprove No Opinion
Republican
84
40
28
Democrat
100
48
36
Independent
20
32
12
Find the expected frequency for the cell E2,2. Round to the nearest tenth if necessary.
A) 93.84
B) 45.6
C) 34.96
D) 55.2
110) The contingency table below shows the results of a random sample of 200 state representatives that
was conducted to see whether their opinions on a bill are related to their party affiliation. Use α =
0.05.
Opinion
Party
Approve Disapprove No Opinion
Republican
42
20
14
Democrat
50
24
18
Independent
10
16
6
2
Find the critical value χ 0 , to test the claim of independence.
A) 11.143
B) 9.488
C) 7.779
D) 13.277
111) A random sample of 400 men and 400 women was randomly selected and asked whether
they planned to vote in the next election. The results are listed below. Perform a
homogeneity of proportions test to test the claim that the proportion of men who plan to
vote in the next election is the same as the proportion of women who plan to vote. Use α =
0.05.
Men Women
Plan to vote
230 255
Do not plan to vote 170 145
15
111)
110)
Answer Key
Testname: FINALEXAMRVIEW
1)
2)
3)
4)
population: collection of all American households; sample: collection of 1353 American households surveyed
It describes a statistic because the number $125,000 is based on a subset of the population.
A
A population is the collection of all outcomes, responses, measurements, or counts that are of interest.. A sample is a
subset of a population.
5) B
6) A
7) D
8) D
9) The study may be biased because it is limited to people with computers.
10) B
11)
12) C
13) Key: 0 4 = 4
0
1
2
3
4
5
6
4 8
0 5
5
3 6 6
0 0 9
0
3 4 6
Most of these years he hit 36 or more home runs.
16
Answer Key
Testname: FINALEXAMRVIEW
14)
15) A
16) mean 86, median 87, mode 88
17) A
18) C
19) D
20) C
21) Battery Type B has less variation. As a result, it is less likely to fail before its mean life is up.
22) B
23) At least 75% of the heights should fall between 58.6 in. and 68.6 in.
24) A
1.82
× 100% = 58.3%
25) coefficient of variation = 3.12
26) D
27) B
28) B
29) C
30) C
31) (hit, miss)
32) B
33) D
34) A
35) B
36) B
37) A
38) B
39) B
40) 0.994
41) A
1
= 0.000001
42)
1,000,000
43) A
44) D
45)
x
1 2 3 4 5 6 7
P(x) 0.71 0.12
0
0.12
0
0
0.06
46) probability distribution
47) C
48) binomial experiment
49) μ = np = 650(0.5) = 325; σ = npq = 650(0.5)(0.5) = 12.75
50) B
51) n = 100; p = 0.5; q = 0.5; x = 0, 1, 2, . . ., 99, 100
17
Answer Key
Testname: FINALEXAMRVIEW
52) D
53) D
54) C
55) About 6 pregnancies
56) z = -0.58
57) C
58) A
59) A
60) B
61) 50/800 = 0.0625 = 6.25%, hence the finite correction factor applies; P(x < 185,000) = 0.9279
62) cannot use normal distribution, nq = (16)(0.1) = 1.6 < 5
63) D
64) P(4.5 < X < 5.5) = P(-3.24 < z <-2.93) = 0.0017 - 0.0006 = 0.0011
65) A
66) C
67) A
68) C
69) (127.0, 133.0)
70) D
71) A
72) B
73) A
74) D
75) H0 : μ = 50.9, Ha : μ ≠ 50.9
76) B
77) type I: rejecting H0 : μ = 57.9 when μ = 57.9
type II: failing to reject H0 : μ = 57.9 when μ ≠ 57.9
78) C
79) B
80) C
81) B
82) B
83) B
84) D
85) D
86) C
87) P-value = 0.4766. Since the P-value is great than α, there is not sufficient evidence to support the the groupʹs claim.
88) B
89) B
90) B
91) Confidence interval (-0.656, 0.056); 0 lies in the interval, fail to reject H0 ; There is not sufficient evidence to support the
claim.
92) B
93) D
94) A
95) C
96) A
97) A
98) B
18
Answer Key
Testname: FINALEXAMRVIEW
99) B
100) explanatory variable: rainfall in inches; response variable: yield per acre
101)
There appears to be a positive linear correlation.
B
The correlation coefficient remains unchanged.
D
The sign of m is unchanged, but the values of m and b change.
11, 26, 32, 21, and 7, respectively.
C
108) Critical value χ 0 2 = 9.488; chi-square test statistic χ 2 = 1.77; fail to reject H0 ; The ages of employees are normally
102)
103)
104)
105)
106)
107)
distributed.
109) D
110) B
2
111) critical value χ 0 = 3.841; chi-square test statistic χ 2 ≈ 3.273; fail to reject H0 ; There is not sufficient evidence to reject
the claim.
19