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final exam, MGT122, summer 2021

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9/7/21, 3:58 PM
final exam, MGT122, summer 2021 (Preview) Microsoft Forms
final exam, MGT122, summer 2021

Points: 2/40
1. A quality control engineer is interested in the mean length of sheet insulation
being cut automatically by machine. The desired mean length of the insulation
is 12 feet. It is known that the standard deviation in the cutting length is 0.15
feet. A sample of 70 cut sheets yields a mean length of 12.14 feet. This sample
will be used to obtain a 99% confidence interval for the mean length cut by
machine. the critical value to use in obtaining the confidence interval is ________.
*
(-/3 Points)
2.58
2. A university dean is interested in determining the proportion of students who
receive some sort of financial aid. Rather than examine the records for all
students, the dean randomly selects 200 students and finds that 118 of them
are receiving financial aid. The 95% confidence interval for π is 0.59 ± 0.07.
Interpret this interval. *
(-/1 Points)
We are 95% confident that the true proportion of all students receiving financial aid
is between 0.52 and 0.66.
95% of the students get between 52% and 66% of their tuition paid for by financial
aid.
We are 95% confident that between 52% and 66% of the sampled students receive
some sort of financial aid.
We are 95% confident that 59% of the students are on some sort of financial aid.
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3. If the outcome of event A is not affected by event B, then events A and B are
said to be *
(-/1 Points)
mutually exclusive.
independent.
collectively exhaustive.
None of the above.
4. A major department store chain is interested in estimating the mean amount its
credit card customers spent on their first visit to the chain’s new store in the
mall. Fifteen credit card accounts were randomly sampled and analyzed with
the following results: mean of the sample =$50.50 and S=20. Assuming the
distribution of the amount spent on their first visit is normal, what is the shape
of the sampling distribution of the sample mean that will be used to create the
desired confidence interval for μ? *
(-/1 Points)
Approximately normal with a mean of $50.50
A standard normal distribution
A t distribution with 15 degrees of freedom
A t distribution with 14 degrees of freedom
5. A major department store chain is interested in estimating the mean amount its
credit card customers spent on their first visit to the chain’s new store in the
mall. Fifteen credit card accounts were randomly sampled and analyzed with
the following results: mean of the sample is $50.50 and S=20. Construct a 95%
confidence interval for the mean amount its credit card customers spent on
their first visit to the chain’s new store in the mall assuming that the amount
spent follows a normal distribution. *
(-/1 Points)
$50.50 ± $9.09
$50.50 ± $10.12
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$50.50 ± $11.00
$50.50 ± $11.08
6. An insurance company evaluates many numerical variables about a person
before deciding on an appropriate rate for automobile insurance. A
representative from a local insurance agency selected a random sample of
insured drivers and recorded, X, the number of claims each made in the last 3
years, with the following results.
Xf
1 14
2 18
3 12
45
51
how many drivers are represented in the sample?
*
(-/1 Points)
5
15
50
40
7. The answer to the question “What is your sleeping bag temperature rating?” is
an example of a ratio scaled variable. *
(-/1 Points)
true
False
8. The head librarian at the Library of Congress has asked her assistant for an
interval estimate of the mean number of books checked out each day. The
assistant provides the following interval estimate: from 740 to 920 books per
day. What is an efficient, unbiased point estimate of the number of books
checked out each day at the Library of Congress? *
(-/1 Points)
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740
920
830
1660
9. If an economist wishes to determine whether there is evidence that mean
family income in a community exceeds $50,000 *
(-/1 Points)
either a one-tail or two-tail test could be used with equivalent results.
a one-tail test should be utilized.
a two-tail test should be utilized.
None of the above.
10. The "middle spread," that is the middle 50% of the normal distribution, is equal
to one standard deviation. *
(-/1 Points)
true
false
11. Microsoft Excel was used on a set of data involving the number of defective
items found in a random sample of 46 cases of light bulbs produced during a
morning shift at a plant. A manager wants to know if the mean number of
defective bulbs per case is greater than 20 during the morning shift. She will
make her decision using a test with a level of significance of 0.10. The following
information was extracted from the Microsoft Excel output for the sample of 46
cases:
n = 46; Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error =
3.82; Null Hypothesis: Hμ≤20; α = 0.10; df = 45; T Test Statistic = 2.09; One-Tail
Test Upper Critical Value = 1.3006; p-value = 0.021; Decision = Reject.
the parameter the manager is interested in is:
*
(-/1 Points)
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the mean number of defective light bulbs per case produced at the plant.
the mean number of defective light bulbs per case among the 46 cases.
the mean number of defective light bulbs per case produced during the morning
shift.
the proportion of cases with defective light bulbs produced at the plant.
12. For a given level of significance, if the sample size is increased but the summary
statistics remain the same, the probability of committing a Type II error will
increase. *
(-/1 Points)
false
true
13. It is possible to directly compare the results of a confidence interval estimate to
the results obtained by testing a null hypothesis if *
(-/1 Points)
a two-tail test for μ is used.
a one-tail test for μ is used.
Both of the previous statements are true.
None of the previous statements is true.
14. The symbol for the level of significance of a statistical test is *
(-/1 Points)
α.
1 – α.
β.
1 – β.
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15. Which of the following statistics is not a measure of central tendency? *
(-/1 Points)
Arithmetic mean.
median
mode
Q3
16. Which of the following would be an appropriate alternative hypothesis? *
(-/1 Points)
The population proportion is less than 0.65.
The sample proportion is less than 0.65.
The population proportion is not less than 0.65.
The sample proportion is not less than 0.65.
17. The chancellor of a major university was concerned about alcohol abuse on her
campus and wanted to find out the proportion of students at her university
who visited campus bars on the weekend before the final exam week. Her
assistant took a random sample of 250 students. The answer on “whether you
visited campus bars on the weekend before the final exam week” from students
in the sample is an example of __________. *
(-/1 Points)
a categorical variable.
a discrete variable.
a continuous variable.
a table of random numbers.
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18. A quality control engineer is interested in the mean length of sheet insulation
being cut automatically by machine. The desired mean length of the insulation
is 12 feet. It is known that the standard deviation in the cutting length is 0.15
feet. A sample of 70 cut sheets yields a mean length of 12.14 feet. This sample
will be used to obtain a 99% confidence interval for the mean length cut by
machine. calculate the confidence interval. show the steps. *
(1/3 Points)
(12.0901 , 12.1899 )
19. If two equally likely events A and B are mutually exclusive and collectively
exhaustive, what is the probability that event A occurs? *
(-/1 Points)
0
.50
1
Cannot be determined from the information given.
20. Which of the following statements about the median is not true? *
(-/1 Points)
It is more affected by extreme values than the arithmetic mean.
It is a measure of central tendency.
It is equal to Q2.
It is equal to the mode in bell-shaped "normal" distributions.
21. The t distribution allows the calculation of confidence intervals for means when
the actual standard deviation is not known. *
(-/1 Points)
True
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False
22. The probability that a standard normal variable Z is positive is ________. *
(1/1 Points)
0.5
23. A type of vertical bar chart in which the categories are plotted in the
descending rank order of the magnitude of their frequencies is called a *
(-/1 Points)
contingency table.
Pareto chart.
stem-and-leaf display.
pie chart.
24. An insurance company evaluates many numerical variables about a person
before deciding on an appropriate rate for automobile insurance. A
representative from a local insurance agency selected a random sample of
insured drivers and recorded, X, the number of claims each made in the last 3
years, with the following results.
Xf
1 14
2 18
3 12
45
51
how many total claims are represented in the sample?
*
(-/1 Points)
15
50
111
250
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25. Which of the following would be an appropriate null hypothesis? *
(-/1 Points)
The mean of a population is equal to 55.
The mean of a sample is equal to 55.
The mean of a population is greater than 55.
Only (a) and (c) are appropriate.
26. Microsoft Excel was used on a set of data involving the number of defective
items found in a random sample of 46 cases of light bulbs produced during a
morning shift at a plant. A manager wants to know if the mean number of
defective bulbs per case is greater than 20 during the morning shift. She will
make her decision using a test with a level of significance of 0.10. The
following information was extracted from the Microsoft Excel output for the
sample of 46 cases:
n = 46; Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error
= 3.82; Null Hypothesis: Hμ≤20; α = 0.10; df = 45; T Test Statistic = 2.09; OneTail Test Upper Critical Value = 1.3006; p-value = 0.021; Decision = Reject.
the manager can conclude that there is sufficient evidence to show that the
mean number of defective bulbs per case is greater than 20 during the
morning shift using a level of significance of 0.10.
*
(-/1 Points)
true
false
27. In its standardized form, the normal distribution *
(-/1 Points)
has a mean of 0 and a standard deviation of 1.
has a mean of 1 and a variance of 0.
has an area equal to 0.5.
cannot be used to approximate discrete probability distributions.
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28. The owner of a local nightclub has recently surveyed a random sample of n =
250 customers of the club. She would now like to determine whether or not the
mean age of her customers is greater than 30. If so, she plans to alter the
entertainment to appeal to an older crowd. If not, no entertainment changes
will be made. The appropriate hypotheses to test are: *
(-/1 Points)
H0:μ≥30 versus H1:μ<30.
H0:μ≤30 versus H1:μ>30.
H0:sample mean ≥30 versus H1: sample mean <30.
H0: sample mean ≤30 versus H1: sample mean >30.
29. A point estimate consists of a single sample statistic that is used to estimate
the true population parameter. *
(-/1 Points)
True
False
30. Which of the following is a continuous quantitative (numerical) variable? *
(-/1 Points)
The color of a student’s eyes
The number of employees of an insurance company
The amount of milk in a 2-liter carton.
The number of gallons of milk sold at the local grocery store yesterday
31. If two events are mutually exclusive, what is the probability that both occur at
the same time? *
(-/1 Points)
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0
.5
1
Cannot be determined from the information given.
32. According to a survey of American households, the probability that the
residents own 2 cars if annual household income is over $50,000 is 80%. Of the
households surveyed, 60% had incomes over $50,000 and 70% had 2 cars. The
probability that the residents of a household own 2 cars and have an income
less than or equal to $50,000 a year is: *
(-/1 Points)
.12
.18
.22
.48
33. Suppose a 95% confidence interval for μ turns out to be (1,000, 2,100). To make
more useful inferences from the data, it is desired to reduce the width of the
confidence interval. Which of the following will result in a reduced interval
width? *
(-/1 Points)
Increase the sample size.
Increase the confidence level.
Increase the population mean.
Increase the sample mean.
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34. Microsoft Excel was used on a set of data involving the number of defective
items found in a random sample of 46 cases of light bulbs produced during a
morning shift at a plant. A manager wants to know if the mean number of
defective bulbs per case is greater than 20 during the morning shift. She will
make her decision using a test with a level of significance of 0.10. The
following information was extracted from the Microsoft Excel output for the
sample of 46 cases:
n = 46; Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error =
3.82; Null Hypothesis: Hμ≤20; α = 0.10; df = 45; T Test Statistic = 2.09; One-Tail
Test Upper Critical Value = 1.3006; p-value = 0.021; Decision = Reject.
what critical value should the manager use to determine the rejection region?
*
(-/1 Points)
1.6794
1.3011
1.3006
0.6800
35. You know that the probability of committing a Type II error (β) is 5%, you can
tell that the power of the test is *
(-/1 Points)
2.5%
95%
97.5%
unknown
36. An entrepreneur is considering the purchase of a coin-operated laundry. The
current owner claims that over the past 5 years, the mean daily revenue was
$675 with a population standard deviation of $75. A sample of 30 days reveals
a daily mean revenue of $625. If you were to test the null hypothesis that the
daily mean revenue was $675 and decide not to reject the null hypothesis, what
can you conclude? *
(-/1 Points)
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There is not enough evidence to conclude that the daily mean revenue was $675.
There is not enough evidence to conclude that the daily mean revenue was not
$675.
There is enough evidence to conclude that the daily mean revenue was $675.
There is enough evidence to conclude that the daily mean revenue was not $675.
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