CMA TEST 2 (S3)
Question 1
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The width of each bar in a histogram corresponds to the
Select one:
differences between the boundaries of the class.
number of observations in each class.
midpoint of each class.
percentage of observations in each class.
Question 2
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At a meeting of information systems officers for regional offices of a national company, a survey was taken to determine the number of employees the officers supervise in the operation of their departments, where X is the number of employees overseen by each information systems officer.
X f
1 7
2 5
3 11
4 8
5 9
Referring to the table, how many regional offices are represented in the survey results?
Select one:
5
11
15
40
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The following are the durations in minutes of a sample of long-distance phone calls made within the continental United States reported by one long-distance carrier.
Time (in minutes) Relative Frequency
0 but less than 5 0.37
5 but less than 10 0.22
10 but less than 15 0.15
15 but less than 20 0.10
20 but less than 25 0.07
25 but less than 30 0.07
30 or more 0.02
Question 3
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Referring to the table, what is the cumulative relative frequency for the percentage of calls that lasted 10 minutes or more?
Select one:
0.16
0.24
0.41
0.90
Question 4
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The smaller the spread of scores around the arithmetic mean,
Select one:
the smaller the interquartile range.
the smaller the standard deviation.
the smaller the coefficient of variation.
All the above.
Question 5
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True or False: The interquartile range is a measure of variation or dispersion in a set of data.
Select one:
True
False
Question 6
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True or False: As a general rule, an observation is considered an extreme value if its Z score is less than 3.
Select one:
True
False
Question 7
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True or False: The probability that a standard normal random variable, Z, is between 1.00 and 3.00 is 0.1574.
Select one:
True
False
Question 8
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For sample size 1, the sampling distribution of the mean will be normally distributed
Select one:
regardless of the shape of the population.
only if the shape of the population is symmetrical.
only if the population values are positive.
only if the population is normally distributed.
Question 9
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True or False: In inferential statistics, the standard error of the sample mean assesses the uncertainty or error of estimation.
Select one:
True
False
Question 10
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Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is put into a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of 8 private colleges in the United States revealed the following endowments (in millions of dollars): 60.2, 47.0, 235.1, 490.0, 122.6, 177.5, 95.4, and 220.0. What value will be used as the point estimate for the mean endowment of all private colleges in the United States?
Select one:
$1,447.8
$180.975
$143.042
$8
Question 11
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True or False: The t distribution is used to construct confidence intervals for the population mean when the population standard deviation is unknown.
Select one:
True
False
Question 12
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A manager of the credit department for an oil company would like to determine whether the average monthly balance of credit card holders is equal to $75. An auditor selects a random sample of 100 accounts and finds that the average owed is $83.40 with a sample standard deviation of $23.65. If you were to conduct a test to determine whether the average balance is different from $75 and decided to reject the null hypothesis, what conclusion could you draw?
Select one:
There is not evidence that the average balance is $75.
There is not evidence that the average balance is not $75.
There is evidence that the average balance is $75.
There is evidence that the average balance is not $75.
Question 13
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True or False: Suppose, in testing a hypothesis about a proportion, the p-value is computed to be 0.043. The null hypothesis should be rejected if the chosen level of significance is 0.05.
Select one:
True
False
Question 14
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The least squares method minimizes which of the following?
Select one:
SSR
SSE
SST
All of the above
Question 15
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Which of the following terms describes the overall long-term tendency of a time series?
Select one:
Trend
Cyclical component
Irregular component
Seasonal component
Question 16
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Blossom’s Flowers purchases roses for sale for Valentine’s Day. The roses are purchased for $10 a dozen and are sold for $20 a dozen. Any roses not sold on Valentine’s Day can be sold for $5 per dozen. The owner will purchase 1 of 3 amounts of roses for Valentine’s Day: 100, 200, or 400 dozen roses. Given 0.2, 0.4, and 0.4 are the probabilities for the sale of 100, 200, or 400 dozen roses, respectively, then the EMV for buying 200 dozen roses is
Select one:
$4,500
$2,500
$1,700
$1,000
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The data below represents the amount of grams of carbohydrates in a sample serving of breakfast cereal.
10 18 24 30 19 22 24 20 18 25 20 22 19
Question 17
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The variance for this data would be Answer grams.
Answer should be between two and four decimal places e.g. 1.23, 1.234, 1.2345 etc.
Please do NOT include units (grams) in your answer.
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In a local cellular phone area, company A accounts for 70% of the cellular phone market, while company B accounts for the remaining 30% of the market. Of the cellular calls made with company A, 2% of the calls will have some sort of interference, while 3% of the cellular calls with company B will have interference.
Question 18
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If a cellular call is selected at random, the probability that it will NOT have interference is Answer ?
Answer should be between two and four decimal places e.g. 0.12, 0.123, 0.1234 etc.
Please do NOT include any units in your answer.
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The manager of a service station is in the process of analyzing the number of times car owners change the oil in their cars. She believes that the average motorist changes his or her car’s oil less frequently than recommended by the owner’s manual (two times per year). In a preliminary survey she asked 15 car owners how many times they changed their car’s oil in the last 12 months. The results are listed below.
1 1 2 0 3
3 0 1 0 1
2 3 1 3 1
Question 19
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The value of the test statistic in this problem is approximately equal to Answer ?
Answer should be between two and four decimal places e.g. 1.23, 1.234, 1.2345 etc.
Please do NOT include any units in your answer.
Question 20
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What would be your decision if a hypothesis test was conducted on this problem with the null hypothesis given as H0 : µ = 2 and the alternate hypothesis given as H1 2?
Select one:
Reject H0 at the 10%, 5% and 1% level of significance.
Reject H0 at the 10% and 5% level of significance but do not reject H0 at the 1% level of significance.
Reject H0 at the 10% level of significance but do not reject H0 at the 5% or 1% level of significance.
Do not reject H0 at either the 10%, 5% or 1% level of significance.
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Refer to the following table which contains the sales (in $,000) for a department store for the first ten months of the year.
Month Sales
January 440
February 480
March 590
April 400
May 500
June 550
July 470
August 500
September 600
October 520
Question 21
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Using a three period moving average (i.e. MA(3)) as a forecasting method, what is the MSE for this forecasting model?
Answer should be between two and four decimal places e.g. 1.23, 1.234, 1.2345 etc.
Please do NOT include any units in your answer.
Answer:
Question 22
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Using simple exponential smoothing (with a smoothing constant of 0.2) as a forecasting method, what is the MSE for this forecast model?
Answer should be between two and four decimal places e.g. 1.23, 1.234, 1.2345 etc.
Please do NOT include any units in your answer.
Answer:
Information
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The ordered list below resulted from taking a sample of 25 batches of 500 computer chips and determining how many in each batch were defective.
Defects
1, 2, 4, 4, 5, 5, 6, 7, 9, 10, 12, 12, 14, 17, 20, 21, 23, 23, 24, 26, 27, 27, 28, 29, 29
Question 23
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If a frequency distribution for the defects data is constructed, using ‘0 but less than 5’ as the first class, what would be the cumulative relative frequency of the ‘20 but less than 25’ class Answer %?
Answer should be a percentage value to whole numbers e.g. 12, 23, 34 etc.
Please do NOT include units (%) in your answer.
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A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is fifty (50) minutes with a standard deviation of forty (40) minutes (the very large standard deviation is due to a variety of factors including a large variation in skills amongst the ‘Do it yourself’ home handyman which is traditionally one of the companies customer base). Suppose a random sample of 64 purchasers of this table saw is taken.
Question 24
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What is the probability that the sample mean will be more than 44 minutes Answer ?
Answer should be to four decimal places which is consistent with the number of decimal places listed in your appendix tables e.g. 0.1234 etc.
Please do NOT include any units in your answer.
Question 25
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A quality control engineer is interested in the mean length of sheet insulation being cut automatically by machine. The desired length of the insulation is 12 metres. It is known that the standard deviation in the cutting length is 0.15 metres. A sample of 144 cut sheets yield a mean length of 12.14 metres. This sample will be used to obtain a 90% confidence interval for the mean length cut by machine.
What are the two limits of the confidence interval?
min = Answer
max = Answer
Answer should be to four decimal places e.g. 1.2345 and 2.3456.
Please do NOT include any units in your answer.
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An insurance company wishes to examine the relationship between income (in $,000) and the amount of life insurance (in $,000) held by families. The company drew a simple random sample of families and obtained the following results:
Family Income Amount of life insurance
A 40 110
B 80 200
C 110 220
D 80 150
E 80 170
F 120 270
G 60 140
H 100 240
I 60 150
J 90 200
Question 26
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What is the least squares estimate of the slope?
Answer should be to four decimal places e.g. 1.2345.
Please do NOT include any units in your answer.
Answer:
Question 27
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What is the least squares estimate of the Y intercept?
Answer should be to four decimal places e.g. 1.2345.
Please do NOT include any units in your answer.
Answer:
Question 28
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What is the prediction for the amount of life insurance for a family whose income is $85,000?
Answer should be to four decimal places and be consistent with your original data set, e.g. if your answer was $75,410.90, you would enter 75.4109 as your answer.
Please do NOT include any units in your answer.
Answer:
Question 29
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What would be the residual (error) term for a family income of $90,000?
Answer should be to four decimal places and be consistent with your original data set e.g. if your answer was $940.90, you would enter 0.9409. If your answer was $9,400.90, you would enter 9.4009 etc.
Please do NOT include any units in your answer.
Answer:
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International Pictures is trying to decide how to distribute its new movie 'Claws'. 'Claws' is the story of an animal husbandry experiment at the University of Southern Queensland that goes astray, with tragic results. An effort to breed meatier chickens somehow produces an intelligent, 200 kilogram chicken that escapes from the lab and terrorises the campus. In a surprise ending the chicken is befriended by coach Tim Galvano, who teaches it how to play Rugby and help his team win State, National and World Championships. Because of the movie's controversial nature, it has the potential to be either a smash hit, a modest success, or a total bomb. International is trying to decide whether to release the picture for general distribution initially or to start out with a 'limited first-run release' at a few selected theatres, followed by general distribution after 3 months. The company has estimated the following probabilities and conditional profits for 'Claws':
PROFITS (Millions of $)
Level of success Probability Limited release General distribution
Smash .3 22 12
Modest .4 9 8
Bomb .3 –10 –2
International can run sneak previews of 'Claws' to get a better idea of the movies' ultimate level of success. Preview audiences rate movies as either good or excellent. On the basis of past experiences, it was found that 90% of all smash successes were rated excellent (and 10% rated good), 75% of all modest successes were rated excellent (25% rated good) and 40% of all bombs were rated excellent (60% rated good). The cost of running sneak previews is not cheap. Currently, this stands at $1m.
Question 30
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What is the opportunity loss for a Limited release for a Bomb level of success?
Answer should be to whole numbers only. You do not need to put any units in your answer.
Answer:
Question 31
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What would the optimal action be for International before running the sneak preview?
Select one:
Run a limited release with an expected payoff of $7.20m
Run a limited release with an expected payoff of $6.20m
Run a general distribution with an expected payoff of $7.20m
Run a general distribution with an expected payoff of $6.20m
Question 32
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What is the maximum amount of money that International would be prepared to pay for an absolutely reliable forecast of the movies’ level of success?
Select one:
$9.6m
$7.2m
$6.2m
$2.4m
Question 33
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What would be the joint probability for a ‘modest success’ and good preview given that in the past, it was found that 25% of all modest successes were rated good?
Answer should be to two decimal places e.g. 0.12, 0.23, etc.
Please do NOT include any units in your answer.
Answer:
Question 34
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What is the posterior probability of a modest success given the sneak preview indicates excellent?
Answer should be to four decimal places e.g. 0.1234, 0.2345 etc.
Please do NOT include any units in your answer.
Answer:
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The tourist industry is subject to enormous seasonal variation. A hotel in North Queensland has recorded its occupancy rate for each quarter during the past 5 years. These data are shown in the accompanying table.
Table 1: Occupancy rate
Year
2004 2005 2006 2007 2008
Quarter 1 0.561 0.575 0.594 0.622 0.665
Quarter 2 0.702 0.738 0.738 0.708 0.835
Quarter 3 0.800 0.868 0.729 0.806 0.873
Quarter 4 0.568 0.605 0.600 0.632 0.670
Question 35
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(All calculations should be to at least three decimal places)
What is the centred moving average that would correspond to Quarter 1 in 2006?
Answer should be consistent with the data provided and be to three decimal places e.g. 0.123, 0.456 etc.
Please do NOT include any units in your answer.
Answer:
Question 36
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(All calculations should be to at least three decimal places)
What is the adjusted seasonal index for Quarter 1 Answer %?
Answer should be listed to three decimal places in the form 0.123 i.e. 0.123 represents 12.3%, 1.234 represents 123.4% etc.
Please do NOT include the units (%) in your answer.
Question 37
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(All calculations should be to at least three decimal places)
The trend line for this decomposition model can be read off the following partial regression printout (at 3 decimal places) to be Y = 0.650 + 0.004 T where T represents time.

Analysing the partial regression printout, what is the coefficient of determination (R2) for this trend line? (Select the closest correct answer).
Select one:
0.0932 (9.32%)
0.3448 (34.48%)
0.4545 (45.45%)
0.5455 (54.55%)
Question 38
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(All calculations should be to at least three decimal places)
What would be the forecast in Quarter 1, 2009 using the trend line previously given (i.e. Y = 0.650 + 0.004 T) and the relevant adjusted seasonal index?
Answer should be consistent with the data provided and be to three decimal places e.g. 0.123, 0.456 etc.
Please do NOT include any units in your answer.
Answer:
Question 39
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(All calculations should be to at least three decimal places)
If we exponentially smooth the data in Table 1 with a smoothing constant of 0.1, the smoothed value for Quarter 4 in 2004 would be?
Answer should be consistent with the data provided and be to three decimal places e.g. 0.123, 0.456 etc.
Please do NOT include any units in your answer.
Answer:
Question 40
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(All calculations should be to at least three decimal places)
If we exponentially smooth the data in Table 1 with a smoothing constant of 0.1, the forecast for Quarter 1 2009 would be?
Answer should be consistent with the data provided and be to three decimal places e.g. 0.123, 0.456 etc.
Please do NOT include any units in your answer.
Answer: