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- From: Mathematics, Statistics and Probability
- Posted on: Fri 22 Jan, 2016
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1
Question: The standard error of the mean for a sample of 100 is 30. In order to cut the standard error of the mean to 15, we would
A increase the sample size to 200
B increase the sample size to 400
C decrease the sample size to 50
D decrease the sample size to 25
2
Question: A probability distribution is an equation that
A Associates a particular probability of occurrence with each outcome in the sample space
B Measures outcomes and assigns values of X to the simple events
C Assigns a value to the variability in the sample space
D Assigns a value to the center of the sample space
3
Question: Elaine’s Famous Quilts sells, surprisingly, quilts. Elaine, always wishing to understand her process and improve quality took a long term assessment of her quilts and determined that, on average, there were 3 quilting errors per quilt. Elaine decided that this was OK as long as she understood the probability of getting more than 4 errors per quilt. As the statistics guru working for Elaine, which distribution should you use to determine that probability?
A Binomial distribution
B Poisson distribution
C Normal distribution
D None of the above
4
Question: The confidence interval obtained will always correctly estimate the population parameter.
A True
B False
5
Question: The next state lottery will have the following payoffs possible with their associated probabilities.
You buy a single ticket. (note, answers may be rounded slightly)
The probability that you win at least $100.00 is ________
A 0.333
B 0.0066
C 0.0666
D 0.1
6
Question: The width of a confidence interval estimate for a proportion will be
A Narrower for 99% confidence than for 95% confidence
B Wider for a sample size of 100 than for a sample size of 50
C Narrower for 90% confidence than for 95% confidence
D Narrower when the sample proportion is 0.50 than when the sample proportion is 0.20
7
Question: For some positive value of Z, the probability that a standard normal variable is between 0 and Z is 0.3770. The value of Z is
A 0.18
B 0.81
C 1.16
D 1.47
8
Question: The standard error of the proportion will become larger
A as p approaches 0
B as p approaches 0.50
C as p approaches 1.00
D as n increases
9
Question: A random sample of 100 stores from a large chain of 1,000 garden supply stores was selected to determine the average number of lawnmowers sold at an end-of-season clearance sale. The sample results indicated an average of 6 and a standard deviation of 2 lawnmowers sold. A 95% confidence interval (5.623 to 6.377) was established based on these results.
If the population had consisted of 10,000 stores, the confidence interval estimate of the mean would have been wider in range.
A True
B False
10
Question: The Central Limit Theorem is important in statistics because
A For a large n, it says the population is approximately normal
B For any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size
C For a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population
D For any sized sample, it says the sampling distribution of the sample mean is approximately normal
11
Question: The largest value that a Poisson random variable X can have is n.
A True
B False
12
Question: A certain type of new business succeeds 60% of the time. Suppose that 3 such businesses open (where they do not compete with each other, so it is reasonable to believe that their relative successes would be independent).
The probability that all 3 businesses succeed is ________
A 0.064
B 0.216
C 0.936
D 0.288
13
Question: It is desired to estimate the average total compensation of CEOs in the Service industry. Data were randomly collected from 18 CEOs and the 97% confidence interval was calculated to be ($2,181,260, $5,836,180). Which of the following interpretations is correct?
A 97% of the sampled total compensation values fell between $2,181,260 and $5,836,180
B We are 97% confident that the mean of the sampled CEOs falls in the interval $2,181,260 to $5,836,180
C In the population of Service industry CEOs, 97% of them will have total compensations that fall in the interval $2,181,260 to $5,836,180
D We are 97% confident that the average total compensation of all CEOs in the Service industry falls in the interval $2,181,260 to $5,836,180
14
Question: A random sample of 100 stores from a large chain of 1,000 garden supply stores was selected to determine the average number of lawnmowers sold at an end-of-season clearance sale. The sample results indicated an average of 6 and a standard deviation of 2 lawnmowers sold. A 95% confidence interval (5.623 to 6.377) was established based on these results.
95% of the stores have sold between 5.623 and 6.377 lawnmowers.
A True
B False
15
Question: In a binomial distribution
A The random variable X is continuous
B The probability of success (p) is stable from trial to trial
C The number of trials (n) must be at least 30
D The results of one trial are dependent on the results of the other trials
16
Question: The probability that a standard normal random variable, Z, is between 1.50 and 2.10 is the same as the probability Z is between -2.10 and -1.50.
A True
B False
17
Question: The Poisson distribution can be used to model a continuous random variable.
A True
B False
18
Question: A certain type of new business succeeds 60% of the time. Suppose that 3 such businesses open (where they do not compete with each other, so it is reasonable to believe that their relative successes would be independent).
The probability that exactly 1 business succeeds is ________
A 0.064
B 0.216
C 0.936
D 0.288
19
Question: The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. What is the probability that the sample mean will be between 39 and 48 minutes?
A 1.0
B 0.3437
C 0.5
D 0.8767
20
Question: A certain type of new business succeeds 60% of the time. Suppose that 3 such businesses open (where they do not compete with each other, so it is reasonable to believe that their relative successes would be independent).
The probability that at least 1 business succeeds is ________
A 0.064
B 0.216
C 0.936
D 0.288
21
Question: The connotation "expected value" or "expected gain" from playing roulette at a casino means
A The amount you expect to "gain" on a single play
B The amount you expect to "gain" in the long run over many plays
C The amount you need to "break even" over many plays
D The amount you should expect to gain if you are lucky
22
Question: The amount of time it takes to complete an examination has a skewed-left distribution with a mean of 65 minutes and a standard deviation of 8 minutes. If 64 students were randomly sampled, the probability that the sample mean of the sampled students exceeds 71 minutes is approximately 0.
A True
B False
23
Question: The standard error of the mean
A Is never larger than the standard deviation of the population
B Decreases as the sample size increases
C Measures the variability of the mean from sample to sample
D All of the above
24
Question: If the mean of a sampling distribution is equal to the parameter it is estimating, then we say that sampling distribution is _____________________.
A Unbiased
B Minimum variance
C Biased
D Random
25
Question: Sampling distributions describe the distribution of
A Parameters
B Statistics
C Both parameters and statistics
D Neither parameters nor statistics
26
Question: Sampling distributions describe the distribution of
A Parameters
B Statistics
C Both parameters and statistics
D Neither parameters nor statistics
27
Question: The t distribution is used to develop a confidence interval estimate of the population mean when the population standard deviation is unknown.
A True
B False
28
Question: 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 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 confidence interval goes from ________ to ________
A 0 to 15 feet
B 12.09 to 12.19 feet
C 7.14 to 17.14 feet
D (12.09 minus .99) to (12.09 plus .99) feet
29
Question: The amount of time necessary for assembly line workers to complete a product is a normal random variable with a mean of 15 minutes and a standard deviation of 2 minutes. So, 90% of the products require more than __________ minutes for assembly.
A 1.0
B 15.0
C 17.6
D 12.4
30
Question: The following table contains the probability distribution for X = the number of retransmissions necessary to successfully transmit a 1024K data package through a double satellite media.
The mean or expected value for the number of retransmissions is ________
A 1.0
B 0.35
C 0.65
D None of the above
31
Question: The Central Limit Theorem allows the use of the Normal distribution to analyze the sample mean if the sample sizes are large enough.
A True
B False
32
Question: A multiple-choice test has 30 questions. There are 4 choices for each question. A student who has not studied for the test decides to answer all questions randomly. What type of probability distribution can be used to figure out his chance of getting at least 20 questions right?
A Binomial distribution
B Poisson distribution
C Normal distribution
D None of the above
33
Question: The confidence interval estimate of the population mean is constructed around the sample mean.
A True
B False
34
Question: A random sample of 100 stores from a large chain of 1,000 garden supply stores was selected to determine the average number of lawnmowers sold at an end-of-season clearance sale. The sample results indicated an average of 6 and a standard deviation of 2 lawnmowers sold. A 95% confidence interval (5.623 to 6.377) was established based on these results.
Of all possible samples of 100 stores drawn from the population of 1,000 stores, 95% of the sample means will fall between 5.623 and 6.377 lawnmowers.
A True
B False
35
Question: Given that X is a normally distributed random variable with a mean of 50 and a standard deviation of 2, find the probability that X is between 47 and 54.
A 1.0
B 0.4552
C 0.9104
D Cannot be determined
36
Question: 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 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.
Suppose the engineer had decided to estimate the mean length to within 0.03 with 99% confidence. Then the sample size would be ________
A 167
B 70
C 56
D 203
37
Question: The next state lottery will have the following payoffs possible with their associated probabilities.
You buy a single ticket. (note, answers may be rounded slightly)
If you have a winning ticket, the probability that you win at least $100.00 is ________
A 0.333
B 0.0066
C 0.0666
D 0.1
38
Question: A food processor packages orange juice in small jars. The weights of the filled jars are approximately normally distributed with a mean of 10.5 ounces and a standard deviation of 0.3 ounce. Find the proportion of all jars packaged by this process that have weights that fall below 10.875 ounces.
A 1.0
B 0.8944
C 0.9104
D 0.3944
39
Question: The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year. The probability that there will be exactly 3 power outages in a year is ____________.
A 0.5
B 3!/6!
C .0892
D Cannot be determined
40
Question: Which of the following statements about the sampling distribution of the sample mean is incorrect?
A If the sample mean is taken from a Normally Distributed Population, then the sampling distribution of the mean will be Normally Distributed.
B
C
D The standard deviation of the sampling distribution of the sample mean is equal to ?
41
Question: If the population distribution is symmetric, the sampling distribution of the mean can be approximated by the normal distribution if the samples contain at least 15 observations.
A True
B False
42
Question: Another name for the mean of a probability distribution is its expected value.
A True
B False
43
Question: As the sample size increases, the standard error of the mean increases
A True
B False
44
Question: The next state lottery will have the following payoffs possible with their associated probabilities.
You buy a single ticket. (note, answers may be rounded slightly)
If the ticket you purchased cost $10.00, what is the expected value of your winning (loss)?
A $4.85
B $-5.15
C $10.00
D Cannot be determined from the information given
45
Question: The following table contains the probability distribution for X = the number of retransmissions necessary to successfully transmit a 1024K data package through a double satellite media.
The probability of no retransmissions is ________
A 1.0
B 0.35
C 0.65
D None of the above
46
Question: If you were constructing a 99% confidence interval of the population mean based on a sample of n = 25 where the standard deviation of the sample s = 0.05, the critical value of t will be
A 2.7969
B 2.7874
C 2.4922
D 2.4851
47
Question: If the population distribution is unknown, in most cases the sampling distribution of the mean can be approximated by the normal distribution if the samples contain at least 30 observations.
A True
B False
48
Question: The following table contains the probability distribution for X = the number of retransmissions necessary to successfully transmit a 1024K data package through a double satellite media.
The probability of at least one retransmission is ________
A 1.0
B 0.35
C 0.65
D None of the above
49
Question: Which of the following is true about the sampling distribution of the sample mean?
A The mean of the sampling distribution is always ?
B
C The shape of the sampling distribution is always approximately normal
D All of the above are true
50
Question: A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts. Suppose the mean cost of rats used in lab experiments turned out to be $13.00 per week. Interpret this value.
A Most of the weeks resulted in rat costs of $13.00
B The median cost for the distribution of rat costs is $13.00
C The expected or average cost for all weekly rat purchases is $13.00
D The rat cost that occurs more often than any other is $13.00
51
Question: A confidence interval was used to estimate the proportion of statistics students that are females. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Based on the interval above, is the population proportion of females equal to 0.60?
A No, and we are 90% sure of it
B No. The proportion is 54.17%
C Maybe. 0.60 is a believable value of the population proportion based on the information above
D Yes, and we are 90% sure of it
52
Question: If the outcomes of a random variable follow a Poisson distribution, then their
A Mean equals the standard deviation
B Median equals the standard deviation
C Mean equals the variance
D Median equals the variance
53
Question: A random sample of 100 stores from a large chain of 1,000 garden supply stores was selected to determine the average number of lawnmowers sold at an end-of-season clearance sale. The sample results indicated an average of 6 and a standard deviation of 2 lawnmowers sold. A 95% confidence interval (5.623 to 6.377) was established based on these results.
We do not know for sure whether the true population mean is between 5.623 and 6.377 lawnmowers sold.
A True
B False
54
Question: A certain type of new business succeeds 60% of the time. Suppose that 3 such businesses open (where they do not compete with each other, so it is reasonable to believe that their relative successes would be independent).
The probability that all 3 businesses fail is ________
A 0.064
B 0.216
C 0.936
D 0.288
55
Question: The next state lottery will have the following payoffs possible with their associated probabilities.
You buy a single ticket. (note, answers may be rounded slightly)
The probability that you win any money is ________
A 0.333
B 0.0066
C 0.0666
D 0.1
56
Question: The true length of boards cut at a mill with a listed length of 10 feet is normally distributed with a mean of 123 inches and a standard deviation of 1 inch. What percentage of the boards will be over 125 inches in length?
A 0% (none will be longer than 125 inches)
B 100% (they will all be longer than 125 inches)
C 2.28% will be longer than 125 inches
D 97.72% will be longer than 125 inches
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