Download Practice Exam for Unit 2

Math 281 Introduction to Statistics
Sample Exam 2 (Chapters 6 - 8)
Name___________________________________
Section/Class Time_______________________
Questions 1 - 12 are multiple choice. You will receive six points for each correct response.
Questions 13 and 14 are short answer (solve problem) and are worth 10 points each. You must show your work. Answers
alone are not considered to be a complete solution. All work must be shown in an organized logical format. Clearly identify
your final answers.
You begin with 8 points.
1) The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation
of 15 days. Which of the following is closest to the probability that a pregnancy lasts at least 300 days?
A) 0.018
B) 0.016
C) 0.983
D) 0.483
2) A math teacher gives two different tests to measure students' aptitude for math. Scores on the first test are
normally distributed with a mean of 25 and a standard deviation of 4.3. Scores on the second test are normally
distributed with a mean of 69 and a standard deviation of 11.6. Assume that the two tests use different scales to
measure the same aptitude. If a student scores 29 on the first test, what would be his equivalent score on the
second test? (That is, find the score that would put him in the same percentile.)
A) 80
B) 73
C) 78
D) 81
3) The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 85 inches,
and a standard deviation of 10 inches. Which of the following is closest to the probability that the mean annual
snowfall during 25 randomly picked years will exceed 87.8 inches?
A) 0.081
B) 0.390
C) 0.003
D) 0.581
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4) Suppose you want to collect sample data with the objective of estimating some population proportion. What is
the minimum size sample you need if you desire a margin of error of no more than 7% and a confidence level of
^
95%? Suppose from a prior study, p is estimated by the decimal equivalent of 90%.
A) 63
B) 71
C) 196
D) 213
5) When 297 college students are randomly selected and surveyed, it is found that 126 own a car. Find a 99%
confidence interval for the true proportion of all college students who own a car.
A) 0.357 < p < 0.491
B) 0.377 < p < 0.471
C) 0.368 < p < 0.480
D) 0.350 < p < 0.498
6) The football coach randomly selected ten players and timed how long each player took to perform a certain
drill. The times (in minutes) were:
5.8 6.5 12.7 12.9 8.7
5.4 12.5 14.1 9.9 8.3
Determine a 95 percent confidence interval for the mean time for all players. Assume the sample is selected
from a normally distributed population.
A) 7.79 < μ < 11.57
B) 5.78 < μ < 7.39
C) 9.68 < μ < 10.97
D) 7.38 < μ < 11.98
7) A manufacturer claims that fewer than 6% of its fax machines are defective. In a random sample of 97 such fax
machines, 5% are defective. Find the P-value for a test of the manufacturer's claim.
A) 0.16
B) 0.32
C) 0.17
D) 0.34
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8) A random sample of 139 forty-year-old men contains 26% smokers. Find the P-value for a test of the claim that
the percentage of forty-year-old men that smoke is 22%.
A) 0.26
B) 0.28
C) 0.15
D) 0.13
9) A researcher is interested in estimating the proportion of voters who favor a tax on e-commerce. Based on a
sample of 250 people, she obtains the following 99% confidence interval for the population proportion p:
0.113 < p < 0.171
Which of the statements below is a valid interpretation of this confidence interval?
A: There is a 99% chance that the true value of p lies between 0.113 and 0.171
B: If many different samples of size 250 were selected and, based on each sample, a confidence interval were
constructed, 99% of the time the true value of p would lie between 0.113 and 0.171
C: If many different samples of size 250 were selected and, based on each sample, a confidence interval were
constructed, in the long run 99% of the confidence intervals would contain the true value of p.
D: If 100 different samples of size 250 were selected and, based on each sample, a confidence interval were
constructed, exactly 99 of these confidence intervals would contain the true value of p.
A) A
B) B
C) C
D) D
10) A researcher wishes to construct a 95% confidence interval for a population mean. She selects a simple random
sample of size n = 20 from the population. The population is normally distributed and σ is known. When
constructing the confidence interval, the researcher should use the normal distribution; however, she incorrectly
uses the t distribution. How does this incorrectly calculated confidence relate to the correct confidence interval?
A) The calculated confidence interval is narrower than the correct confidence interval.
B) The calculated confidence interval is shifted to the right of the correct confidence interval.
C) The calculated confidence interval is shifted to the left of the correct confidence interval.
D) The calculated confidence interval is wider than the correct confidence interval.
11) Carter Motor Company claims that its new sedan, the Libra, will average better than 26 miles per gallon in the
city. 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 support the claim that the mean is less than 26 miles per gallon.
B) There is not sufficient evidence to support the claim that the mean is greater than 26 miles per gallon.
C) There is sufficient evidence to support the claim that the mean is less than 26 miles per gallon.
D) There is sufficient evidence to support the claim that the mean is greater than 26 miles per gallon.
12) A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz. Assume that a
hypothesis test of the claim will be conducted. Consider the following statement:
The P-value of the test is the probability that mean weight of the cereal packets this company produces is at
least 14 oz.
A) True
B) False
C) Not enough information given to answer the question.
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Test the claim using the P-value method of hypothesis testing. Be sure to show your work and clearly identify the null
hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that
addresses the original claim. Assume that the sample has been randomly selected from a population with a normal
distribution.
13) A manufacturer makes ball bearings that are supposed to have a mean weight of 30 g. A retailer suspects that
the mean weight is actually less than 30.0 g. The mean weight for a random sample of 16 ball bearings is 29.1 g
with a standard deviation of 4.5 g. At the 0.05 significance level, test the claim that the mean is less than 30.0 g.
14) In tests of a computer component, it is found that the mean time between failures is 520 hours. Suppose a
modification is made to the manufacturing process for this component and you want to determine if the time
between failures has changed. Suppose you test a random sample of 10 modified components and you get the
following times (in hours) between failures.
518
548
521
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
still 520 hours.
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Answer Key
Testname: EX2SAMPLE6_8
1) B
2) A
3) A
4) B
5) D
6) D
7) D
8) A
9) C
10) D
11) D
12) B
13) H0: μ = 30.0 g;
H1 : μ < 30.0 g.
Test statistic: t = -0.80;.
P-value: 0.22. Because the P-value of 0.22 is greater than the significance level of α = 0.05, we fail to reject the null
hypothesis. There is not sufficient evidence to support the claim that the mean is less than 30 g.
14) H0: μ = 520 hours;
H1 : μ ≠ 520 hours
Test statistic: t = 2.14;.
P-value: 0.06. Because the P-value of 0.06 is greater than the significance level of α = 0.05, we fail to reject the null
hypothesis. There is not sufficient evidence to warrant rejection of your claim that the mean is still 520 hours.
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