Statistics Final Exam Review
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Assume that X has a normal distribution, and find the indicated probability.
1) The mean is μ = 60.0 and the standard deviation is σ = 4.0.
Find the probability that X is less than 53.0.
A) 0.9599
B) 0.0802
C) 0.0401
2) The mean is μ = 15.2 and the standard deviation is σ = 0.9.
Find the probability that X is greater than 15.2.
A) 1.0000
B) 0.0003
C) 0.5000
3) The mean is μ = 15.2 and the standard deviation is σ = 0.9.
Find the probability that X is between 14.3 and 16.1.
A) 0.8413
B) 0.6826
C) 0.1587
1)
D) 0.5589
2)
D) 0.9998
3)
D) 0.3413
Solve the problem.
4) The amount of rainfall in January in a certain city is normally distributed with a mean of 4.6 inches
and a standard deviation of 0.3 inches. Find the value of the quartile Q1 .
A) 4.8
B) 4.5
C) 4.4
4)
D) 1.2
Find the indicated probability.
5) The weekly salaries of teachers in one state are normally distributed with a mean of $490 and a
standard deviation of $45. What is the probability that a randomly selected teacher earns more than
$525 a week?
A) 0.2177
B) 0.1003
C) 0.7823
D) 0.2823
Solve the problem.
6) The amount of snowfall falling in a certain mountain range is normally distributed with a mean of
74 inches, and a standard deviation of 12 inches. What is the probability that the mean annual
snowfall during 36 randomly picked years will exceed 76.8 inches?
A) 0.0808
B) 0.4192
C) 0.5808
D) 0.0026
7) The weights of the fish in a certain lake are normally distributed with a mean of 12 lb and a
standard deviation of 12. If 16 fish are randomly selected, what is the probability that the mean
weight will be between 9.6 and 15.6 lb?
A) 0.0968
B) 0.4032
C) 0.6730
D) 0.3270
5)
6)
7)
Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.
8) A certain question on a test is answered correctly by 22% of the respondents. Estimate the
8)
probability that among the next 150 responses there will be at most 40 correct answers.
A) 0.8997
B) 0.0694
C) 0.1003
D) 0.9306
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SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Construct a normal probability plot of the given data. Use your plot to determine whether the data come from a normally
distributed population.
9) The systolic blood pressure (in mmHg) is given below for a sample of 12 men aged
9)
between 60 and 65.
127 135 118 164
143 130 125 153
120 173 140 180
y
x
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
10) Find the critical value z α/2 that corresponds to a degree of confidence of 98%.
A) 2.575
B) 2.05
C) 2.33
10)
D) 1.75
Find the margin of error for the 95% confidence interval used to estimate the population proportion.
11) n = 169, x = 107
A) 0.00269
B) 0.0727
C) 0.127
D) 0.0654
12) In a survey of 4100 T.V. viewers, 20% said they watch network news programs.
A) 0.0122
B) 0.0160
C) 0.0140
D) 0.00915
11)
12)
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
13) n = 58, x = 28; 95 percent
13)
A) 0.353 < p < 0.613
B) 0.375 < p < 0.591
C) 0.374 < p < 0.592
D) 0.354 < p < 0.612
^
Find the minimum sample size you should use to assure that your estimate of p will be within the required margin of
error around the population p.
^
^
14) Margin of error: 0.002; confidence level: 93%; p and q unknown
A) 204,756
B) 204,757
C) 410
14)
D) 409
^
15) Margin of error: 0.01; confidence level: 95%; from a prior study, p is estimated by the decimal
equivalent of 69%.
A) 26,507
B) 8218
C) 14,184
D) 7396
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15)
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
16) When 306 college students are randomly selected and surveyed, it is found that 115 own a car. Find 16)
a 99% confidence interval for the true proportion of all college students who own a car.
A) 0.330 < p < 0.421
B) 0.322 < p < 0.430
C) 0.305 < p < 0.447
D) 0.311 < p < 0.440
17) Of 129 randomly selected adults, 32 were found to have high blood pressure. Construct a 95%
confidence interval for the true percentage of all adults that have high blood pressure.
A) 15.9% < p < 33.7%
C) 17.4% < p < 32.3%
17)
B) 15.0% < p < 34.6%
D) 18.5% < p < 31.1%
Solve the problem.
18) A newspaper article about the results of a poll states: "In theory, the results of such a poll, in 99
cases out of 100 should differ by no more than 6 percentage points in either direction from what
would have been obtained by interviewing all voters in the United States." Find the sample size
suggested by this statement.
A) 461
B) 19
C) 268
D) 378
18)
Determine whether the given conditions justify using the margin of error E = z α/2 σ/ n when finding a confidence
interval estimate of the population mean μ.
19) The sample size is n = 286 and σ = 15.
19)
A) No
B) Yes
Use the confidence level and sample data to find the margin of error E.
20) Weights of eggs: 95% confidence; n = 47, x = 1.44 oz, σ = 0.39 oz
A) 6.86 oz
B) 0.09 oz
C) 0.11 oz
20)
D) 0.02 oz
Use the confidence level and sample data to find a confidence interval for estimating the population μ.
21) Test scores: n = 109, x = 79.1, σ = 6.9; 99 percent
A) 77.8 < μ < 80.4
B) 77.4 < μ < 80.8
21)
C) 78.0 < μ < 80.2
D) 77.6 < μ < 80.6
22) A laboratory tested 90 chicken eggs and found that the mean amount of cholesterol was 230
milligrams with σ = 16.0 milligrams. Construct a 95 percent confidence interval for the true mean
cholesterol content, μ, of all such eggs.
A) 227 < μ < 233
B) 226 < μ < 233
C) 228 < μ < 234
D) 226 < μ < 232
22)
Use the margin of error, confidence level, and standard deviation σ to find the minimum sample size required to estimate
an unknown population mean μ.
23) Margin of error: $121, confidence level: 95%, σ = $528
23)
A) 64
B) 4
C) 2
D) 74
Do one of the following, as appropriate: (a) Find the critical value z α/2, (b) find the critical value tα/2, (c) state that
neither the normal nor the t distribution applies.
24) 99%; n = 17; σ is unknown; population appears to be normally distributed.
A) z α/2 = 2.567
B) tα/2 = 2.921
C) z α/2 = 2.583
25) 98%; n = 7; σ = 27; population appears to be normally distributed.
A) z α/2 = 2.33
B) tα/2 = 2.575
C) z α/2 = 2.05
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24)
D) tα/2 = 2.898
25)
D) tα/2 = 1.96
Find the margin of error.
_
26) 95% confidence interval; n = 91 ; x = 72, s = 11.4
A) 4.57
B) 2.03
26)
C) 2.13
D) 2.37
Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume
that the population has a normal distribution.
27) n = 30, x = 86.5, s = 10.3, 90 percent
A) 82.65 < μ < 90.35
C) 83.31 < μ < 89.69
27)
B) 83.32 < μ < 89.68
D) 81.32 < μ < 91.68
28) A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 193
milligrams with s = 15.4 milligrams. Construct a 95 percent confidence interval for the true mean
cholesterol content of all such eggs.
A) 183.1 < μ < 202.9
B) 183.2 < μ < 202.8
C) 183.3 < μ < 202.7
D) 185.0 < μ < 201.0
28)
Solve the problem.
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29) Find the critical value χ R corresponding to a sample size of 11 and a confidence level of 90
percent.
A) 3.94
B) 18.307
C) 25.188
29)
D) 23.209
Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ.
Assume that the population has a normal distribution.
30) Weights of men: 90% confidence; n = 14, x = 160.9 lb, s = 12.6 lb
A) 9.9 lb < σ < 16.3 lb
B) 9.6 lb < σ < 18.7 lb
C) 10.2 lb < σ < 2.7 lb
D) 9.3 lb < σ < 17.7 lb
30)
Find the appropriate minimum sample size.
31) You want to be 99% confident that the sample standard deviation s is within 5% of the population
standard deviation.
A) 2,638
B) 2,434
C) 923
D) 1,335
31)
Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ.
Assume that the population has a normal distribution.
32) The daily intakes of milk (in ounces) for ten randomly selected people were:
32)
19.8 15.4 25.5 15.5 20.5
24.6 15.6 31.0 28.0 21.4
Find a 99 percent confidence interval for the population standard deviation σ.
A) (3.38, 11.20)
B) (0.83, 3.28)
C) (3.27, 11.20)
D) (3.38, 12.46)
Express the null hypothesis H0 and the alternative hypothesis H1 in symbolic form. Use the correct symbol (μ, p, σ )for
the indicated parameter.
33) A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO,
p, is less than 2 in every one thousand.
A) H0 : p < 0.002
B) H0 : p = 0.002
C) H0 : p = 0.002
D) H0 : p > 0.002
H1 : p ≥ 0.002
H1 : p > 0.002
H1 : p < 0.002
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H1 : p ≤ 0.002
33)
34) Carter Motor Company claims that its new sedan, the Libra, will average better than 30 miles per
gallon in the city. Use μ, the true average mileage of the Libra.
A) H0 : μ = 30
B) H0 : μ < 30
C) H0 : μ = 30
D) H0 : μ > 30
H1 : μ < 30
H1 : μ ≥ 30
H1 : μ > 30
35) A researcher claims that 62% of voters favor gun control.
A) H0 : p = 0.62
B) H0 : p ≥ 0.62
C) H0 : p ≠ 0.62
H1 : p ≠ 0.62
H1 : p < 0.62
H1 : p = 0.62
34)
H1 : μ ≤ 30
35)
D) H0 : p < 0.62
H1 : p ≥ 0.62
Use the given information to find the P-value.
36) The test statistic in a left-tailed test is z = -1.83.
A) 0.0443
B) 0.0336
C) 0.4326
D) 0.4232
37) The test statistic in a two-tailed test is z = 1.95.
A) 0.3415
B) 0.0512
C) 0.4423
D) 0.0244
36)
37)
Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim.
38) A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz.
Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject
the null hypothesis, state the conclusion in nontechnical terms.
A) There is not sufficient evidence to warrant rejection of the claim that the mean weight is at
least 14 oz.
B) There is not sufficient evidence to warrant rejection of the claim that the mean weight is less
than 14 oz.
C) There is sufficient evidence to warrant rejection of the claim that the mean weight is less than
14 oz.
D) There is sufficient evidence to warrant rejection of the claim that the mean weight is at least
14 oz.
38)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final
conclusion that addresses the original claim.
39) Various temperature measurements are recorded at different times for a particular city.
39)
The mean of 20°C is obtained for 40 temperatures on 40 different days. Assuming that σ =
1.5°C, test the claim that the population mean is 23°C. Use a 0.05 significance level.
Test the given claim using the traditional method of hypothesis testing. Assume that the sample has been randomly
selected from a population with a normal distribution.
40) In tests of a computer component, it is found that the mean time between failures is 520
40)
hours. A modification is made which is supposed to increase the time between failures.
Tests on a random sample of 10 modified components resulted in the following times (in
hours) between failures.
518
548
561
523
536
499
538
557
528
563
At the 0.05 significance level, test the claim that for the modified components, the mean
time between failures is greater than 520 hours.
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Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the
sample has been randomly selected.
41) The standard deviation of math test scores at one high school is 16.1. A teacher claims that
41)
the standard deviation of the girls' test scores is smaller than 16.1. A random sample of 22
girls results in scores with a standard deviation of 14.3. Use a significance level of 0.01 to
test the teacher's claim.
42)
a)
An Accountemps survey of 150 executives showed that 44% of them say that
“little or no knowledge of the company” is the most common mistake made
by candidates during job interviews. Use a 0.05 significance level to test the
claim that less than half of all executives identify that error as being the most
common job interviewing error.
b)
Glamour magazine sponsored a survey of 2500 prospective brides and found
that 60% of them spent less than $750 on their wedding gown. Use a 0.01
significance level to test the claim that less than 62% of brides spend less than
$750 on their wedding gown.
c)
A student of the author randomly selected 70 packets of sugar and weighed
the contents of each packet, getting a mean of 3.586 grams and a standard
deviation of 0.074 grams. Test the claim that the weights of the sugar packets
have a mean equal to 3.5 grams, as indicated on the label.
d)
The Orange County Bureau of Weights and Measures received complaints that
the Windsor Bottling Company was cheating consumers by putting less than
12 ounces of root beer in its cans. When 24 cans are randomly selected and
measured, the amounts are found to have a mean of 11.4 ounces and a
standard deviation of 0.62 ounces. Use the sample data to test the claim that
consumers are being cheated.
e)
In clinical tests of the drug Lipitor, 863 patients experience flu symptoms. Use
a 0.01 significance level to test the claim that the percentage of treated patients
with flu symptoms is greater than the 1.9% rate for patients not given the
treatment.
f)
For a simple random sample of adults, IQ scores are normally distributed with
a mean of 100 and a standard deviation of 15. A simple random sample of 13
statistics professors yields a standard deviation of s=7.2. A psychologist is
quite sure that statistics professors have IQ scores that have a mean greater
than 100. He claims that statistics professors have IQ scores with a standard
deviation equal to 15, the same standard deviation for the general population.
Assume that IQ scores of statistics professors are normally distributed and use
a 0.05 significance level to test the claim that σ = 15.
g)
A calculator randomly generates 50 numbers with μ = 100 and σ = 15. One
such generated sample of 50 values has a mean of 98.4 and a standard
deviation of 16.3. Use a .10 significance level to test the claim that the sample
actually does come from a population with a mean equal to 100.
h)
A premed student plans to collect her sample to test the claim that the mean
body temperature is less than 98.6 degrees, as is commonly believed. She
collects data froom 12 people. She measures their body temperatures and
obtains 12 scores not listed below. Use a 0.05 significance level to test the
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42)
claim that these body temperatures come from a population with a mean that
is less than 98.6 degrees.
i)
Women have heights with a mean of 64.1 inches and a standard deviation of
2.52 inches. The sample of 40 heights have a mean of 63.20 inches and a
standard deviation of 2.74 inches. Use a 0.05 significance level to test the claim
that this sample is from a population with a standard deviation equal to 2.52
inches.
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Answer Key
Testname: STATISTICS FINAL EXAM REVIEW
1)
2)
3)
4)
5)
6)
7)
8)
9)
C
C
B
C
A
A
C
D
Because the points lie roughly on a straight line, it appears that the data come from a normally distributed population.
10) C
11) B
12) A
13) D
14) B
15) B
16) C
17) C
18) A
19) B
20) C
21) B
22) A
23) D
24) B
25) A
26) D
27) C
28) B
29) B
30) B
31) D
32) D
33) C
34) C
8
Answer Key
Testname: STATISTICS FINAL EXAM REVIEW
35) A
36) B
37) B
38) D
39) H0 : μ = 23; H1 : μ > 23. Test statistic: z = -12.65;.
P-value: 0.0001. Because the P-value of 0.0001 is less than the significance level of α = 0.05, we reject the null
hypothesis.
40) Test statistic: t = 2.612. Critical value: t = 1.833. Reject H0 . There is sufficient evidence to support the claim that the
mean is greater than 520 hours.
41) Test statistic: X2 = 16.567. Critical value: X 2 = 8.897. Fail to reject H0 . There is not sufficient evidence to support the
claim that the standard deviation of the girls' test scores is smaller than 16.1.
42)
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