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Q:
Systematic sampling is generally similar to simple random sampling in its statistical properties.
Q:
The sampling distribution of the mean will have the same standard deviation as the original population from which the samples were drawn.
Q:
The sampling distribution of the mean will have the same mean as the original population from which the samples were drawn.
Q:
Estimation is the process of inferring the value of an unknown population parameter using data from a random sample
Q:
An estimator is said to be unbiased if the mean of its sampling distribution equals the value of the population parameter being estimated.
Q:
It is customary to approximate the standard error of the sample mean by substituting the sample standard deviation s for in the formula: SE() = .
Q:
The standard error of sample mean is large when the observations in the population are spread out (large ), but that the standard error can be reduced by taking a smaller sample.
Q:
Ideally, we prefer estimates that have large standard errors.
Q:
The standard error of an estimate is the standard deviation of the sampling distribution of the estimate. It measures how much estimates from different samples vary.
Q:
A probability sample is a sample in which the sampling units are chosen from the population by means of a random mechanism such as a random number table.
Q:
An unbiased estimate is a point estimate such that the mean of its sampling distribution is equal to the true value of the population parameter being estimated.
Q:
The sampling distribution of any point estimate (such as the sample mean or proportion) is the distribution of the point estimates we would obtain from all possible samples of a given size drawn from the population.
Q:
One obvious advantage of stratified sampling is that we obtain separate estimates within each stratum " which we would not obtain if we took a simple random sample from the entire population. A more important advantage is that we can increase the accuracy of the resulting population estimates by using appropriately defined strata.
Q:
An interval estimate is an interval calculated from the population data, where we strongly believe the true value of the population parameter lies.
Q:
The difference between the point estimate and the true value of the population parameter being estimated is called the estimation error.
Q:
A point estimate is a single numeric value, a "best guess" of a population parameter, calculated from the sample data.
Q:
Cluster sampling is often less convenient and more costly than other random sampling methods.
Q:
In cluster sampling, the population is divided into subsets called clusters (such as cities or city blocks), and then a random sample of the clusters is selected. Once the clusters are selected, we typically sample all of the members in each selected cluster.
Q:
In stratified sampling with proportional sample sizes, the proportion of each stratum selected differs from stratum to stratum.
Q:
Stratified samples are typically not used in real applications because they provide less accurate estimates of population parameters for a given sampling cost.
Q:
In stratified sampling, the population is divided into relatively homogeneous subsets called strata, and then random samples are taken from each stratum.
Q:
A sample of size 20 is selected at random from a population of size N. If the finite population correction factor is 0.9418, then N must be 169.
Q:
In systematic sampling, one of the first k members is selected randomly, and then every kth member after this one is selected. The value k is called the sampling interval and equals the ratio N / n, where N is the population size and n is the desired sample size.
Q:
A list of all members of the population from which we can choose a sample is called a frame, and the potential sample members are called sampling units.
Q:
A simple random sample is one where each member of the population has a known chance (this may differ from one member to another) or probability of being chosen.
Q:
Simple random samples are typically used in real applications.
Q:
Simple random sampling can result in under-representation or over-representation of certain segments of the population. This is one of several reasons that simple random samples are almost never used in real applications.
Q:
If a simple random sample of size n is chosen from a population of size N, then each member of the population has probability N / n of being chosen in the sample.
Q:
When we sample less than 5% of the population, the finite population correction factor; fpc = , is used to modify the formula for the standard error of the sample mean.
Q:
We can measure the accuracy of judgmental samples by applying some simple rules of probability. This way, judgmental samples are not likely to contain our built-in biases.
Q:
The primary advantage of cluster sampling is sampling convenience (and possibly less cost). The downside, however, is that the inferences drawn from a cluster sample can be less accurate, for a given sample size, than for other sampling plans.
Q:
The averaging effect means that as you average more and more observations from a given distribution, the variance of the average
a. increases
b. decreases
c. is unaffected
d. could either increase, decrease or stay the same
Q:
The Central Limit Theorem (CLT) is generally valid for:
a. n > 5
b. n > 10
c. n > 20
d. n > 30
e. any size n
Q:
The reason the Central Limit Theorem (CLT) is such an important result in statistics is because:
a. The CLT allows us to assume that the population distribution is approximately normal, provided n is reasonably large
b. The CLT allows us to estimate the population mean without knowing the exact form of the population distribution, providedn is reasonably large
c. The CLT allows us to construct confidence intervals for the population mean without knowing the exact form of the population distribution, providedn is reasonably large
d. All of these options
Q:
The finite population correction factor, , should generally be used when:
a. N is any finite size
b. n is less than 5% of the population sizeN
c. n is greater than 5% of the population sizeN
d. n is any finite size
Q:
The approximate 95% confidence interval for a population mean is:
a. b. c. d.
Q:
The approximate standard error of the sample mean is calculated as:
a. b. c. d.
Q:
With proportional sample sizes:
a. The proportion of a stratum in the sample is independent of the proportion of that stratum in the population
b. The proportion of a stratum in the sample is the same as the proportion of that stratum in the population
c. The proportion of a stratum in the sample is greater than the proportion of that stratum in the population
d. The proportion of a stratum in the sample is less than the proportion of that stratum in the population
Q:
If systematic sampling is chosen as the sampling technique, it is probably because:
a. Systematic sampling has better statistical properties than simple random sampling
b. Systematic sampling is more convenient
c. Systematic sampling always results in more representative sampling than simple random sampling
d. None of these options
Q:
Which of the following are reasons for why simple random sampling is used infrequently in real applications?
a. Samples can be spread over a large geographic region
b. Simple random sampling requires that all sampling units be identified prior to sampling
c. Simple random sampling can result in underrepresentation or overrepresentation of certain segments of the population
d. All of these options
Q:
Which of the following statements are correct?
a. An interval estimate describes a range of values that is likely not to include the actual population parameter
b. An interval estimate is an estimate of the range for a sample statistic.
c. An interval estimate is an estimate of the range of possible values for a population parameter.
d. None of these options
Q:
An unbiased estimator is a:
a. sample statistic used to approximate a population parameter
b. sample statistic, which has an expected value equal to the value of the population parameter
c. sample statistic whose value is usually less than the population parameter
d. standard error of the mean
Q:
Which of the following statements are correct?
a. A point estimate is an estimate of the range of a population parameter
b. A point estimate is a single value estimate of the value of a population parameter
c. A point estimate is an unbiased estimator if its standard deviation is the same as the actual value of the population standard deviation
d. All of these options
Q:
There is approximately _____ % chance that any particular will be within two standard deviations of the population mean ().
a. 90
b. 95
c. 99
d. 99.7
Q:
A list of all members of the population is called a:
a. sampling unit
b. probability sample
c. frame
d. relevant population
Q:
The theorem that states that the sampling distribution of the sample mean is approximately normal when the sample size n is reasonably large is known as the:
a. central limit theorem
b. central tendency theorem
c. simple random sample theorem
d. point estimate theorem
Q:
The opportunity for sampling error is decreased by:
a. larger sample sizes
b. smaller sample sizes
c. affluent samples
d. educated samples
Q:
Sampling error is evident when:
a. a question is poorly worded
b. the sample is too small
c. the sample is not random
d. the sample mean differs from the population mean
Q:
The two basic sources for error when using random sampling are:
a. sampling and selection
b. identification and selection
c. sampling and nonsampling
d. bias and randomness
e. linear and nonlinear
Q:
Measurement error occurs when:
a. a portion of the sample does not respond to the survey
b. the sample responses are not clear
c. the responses to question do not reflect what the investigator had in mind
d. the investigator does not correctly tally all responses
Q:
Non-truthful response is a particular problem when:
a. sensitive questions are asked.
b. surveys are anonymous.
c. interviewers are not trained.
d. the sample is from an unusual population.
Q:
The sampling mean is the _____ estimate for the population mean.
a. random
b. point
c. simple
d. interval
Q:
The accuracy of the point estimate is measured by its:
a. standard deviation
b. standard error
c. sampling error
d. nonsampling error
Q:
When a portion of the sample does not respond to the survey, _____ results.
a. measurement error
b. nonresponse bias
c. sampling error
d. systematic failure
e. nonlinear error
Q:
The opportunity for nonsampling error is increased by:
a. larger sample sizes
b. smaller sample sizes
c. affluent samples
d. educated samples
Q:
The standard deviation of is usually called the
a. standard error of the mean
b. standard error of the sample
c. standard error of the population
d. randomized standard error
Q:
A sampling error is the result of:
a. measurement error
b. nonresponse bias
c. nontruthful responses
d. bad luck
Q:
The key to using stratified sampling is:
a. identifying the strata
b. selecting the appropriate strata
c. defining the strata
d. randomizing the strata
Q:
In sampling, a population is:
a. the set of all humans
b. the set of all members about which a study intends to make inferences
c. any group of test subjects
d. a random group of individuals, households, cities or countries
Q:
Potential sample members, called sampling units, are:
a. people
b. companies
c. households
d. All of these options
Q:
Selecting a random sample from each identifiable subgroup within a population is called:
a. random sampling
b. systematic sampling
c. stratified sampling
d. cluster sampling
e. None of these options
Q:
The probability of being chosen in a simple random sample of size n from a population of size N is:
a. 1/N
b. N " 1/n
c. N/n
d. n/N
Q:
The defining property of a simple random sample is that:
a. every sample has the same chance of being chosen
b. the easiest method to access samples are chosen
c. the fewest samples are chosen
d. every fourth subject is chosen as a sample
Q:
A judgmental sample is a sample in which the
a. sampling units are chosen using a random number table
b. quality of sampling units judged
c. sampling units are chosen according to the sampler's judgment
d. sampling units are all biased and vocal about it
Q:
A sample in which the sampling units are chosen from the population by means of a random mechanism is a
a. probability sample
b. judgmental sample
c. stratified sample
d. systematic sample
Q:
Identifiable subpopulations within a population are called:
a. clusters
b. samples
c. blocks
d. strata
e. None of these options
Q:
Which of the following is not a consideration when determining appropriate sample size?
a. The cost of sampling
b. The timely collection of the data
c. Interviewer fatigue
d. The likelihood of nonsampling error
Q:
The sampling method in which a population is divided into blocks and then selected by choosing a random mechanism is called a
a. random sampling
b. systematic sampling
c. stratified sampling
d. cluster sampling
Q:
The mean of the sampling distribution of always equals
a. the population mean
b. / n
c. the population standard deviation d. / n
Q:
A sample chosen in such a way that every possible subset of same size has an equal chance of being selected is called a(n)
a. interval estimation
b. point estimation
c. simple random sample.
d. statistic
Q:
Which of the following statements correctly describe estimation?
a. It is the process of inferring the values of known population parameters from those of unknown sample statistics.
b. It is the process of inferring the values of unknown sample statistics from those of known population parameters.
c. It is the process of inferring the values of known sample statistics from those of unknown population parameters.
d. It is the process of inferring the values of unknown population parameters from those of known sample statistics.
Q:
NARRBEGIN: SA_69_72
A recent MBA graduate is considering an offer of employment at a biotech company, where she has been offered stock options as part of her compensation package. The options give her the right, but not the obligation, to buy 2500 shares of stock either one year from now or two years from now at a price of $50, which is the current market price of the stock. If the price of the stock has risen above $50 at either time, she can buy 2500 shares at $50 and then immediately sell at the current price, thereby making a risk-free profit. On the other hand, if the price of the stock has dropped below $50, she will not exercise the option because it is "out of the money" and she would loose money. Based on historical market information, she estimates that the stock price in the first year will either go up by 25% from its current price, with probability of 0.55, or it will go down by 15%, with probability of 0.45. In either case, she can exercise the options or wait to see what will happen in the second year. If she decides to wait, the in the second year, the stock price will again go up or down by the same amounts and with the same probabilities, starting from either the "up" or "down" price at the end of the first year.
NARREND
(A) Construct a decision tree to help her model her option decision making. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.
(B) What is the optimal decision making policy regarding the options in all possible scenarios over the next two years?
(C) What is the expected value of the stock options? Ignore the time value of money (assume no discounting of future payoffs)
(D) If her estimates of the increases/decreases or probabilities are inaccurate, could the options have a negative EMV?
Q:
NARRBEGIN: SA_66_68
A construction company has obtained a contract for a highway project and will need to lease an additional road grader for a month to fill out its equipment fleet. The company is trying to decide between two different lease options for the grader: 1) lease an older grader for $8,500, or 2) lease a newer grader for $10,000. The newer grader is still under warranty, so the lease cost covers all repair expenses. However, the company would be responsible for any repair expenses if it leases the older grader. The construction company's maintenance foreman believes there is a 30% chance that there will be no need for repairs with the older grader, but also thinks there is a 45% chance that some repairs ($2,000) could be needed, and a 25% chance that significant repairs ($5,000) might be required.
NARREND
(A) Construct a decision tree to help the company make its decision. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.
(B) What is the best lease option? Why?
(C) Suppose the company could hire an experienced mechanic to inspect the old grader to determine the repair cost before the company makes its final decision. If the mechanic is always correct in his assessments, what is the most the company would pay for the inspection?
Q:
NARRBEGIN: SA_63_65
An investor has $25,000 in assets and faces a difficult choice between two investments. If he invests in the first opportunity there is a 70% chance that he will increase his assets by $75,000 and a 30% chance that he will increase his assets by $20,000. If he invests in the second option there is a 40% chance that he will increase his assets by $150,000 and a 60% chance that he will increase his assets by $5,000.
NARREND
(A) Construct a decision tree to help the investor make his decision. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.
(B) What is the best choice for the investor? Why?
(C) Suppose that investor has an exponential utility function for final assets with a risk tolerance parameter equal to $60,000. Which investment opportunity will he prefer in this case? What is his certainty equivalent?
Q:
NARRBEGIN: SA_55_62A landowner in Texas is offered $200,000 for the exploration rights to oil on her land, along with a 25% royalty on the future profits if oil is discovered. The landowner is also tempted to develop the field herself, believing that the interest in her land is a good indication that oil is present. In that case, she will have to contract a local drilling company to drill an exploratory well on her own. The cost for such a well is $750,000, which is lost forever if no oil is found. If oil is discovered, however, the landowner expects to earn future profits of $7,500,000. Finally, the landowner estimates (with the help of her geologist friend) the probability of finding oil on this site to be 60%.NARREND(A) Construct a decision tree to help the landowner make her decision. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.(B) What should the landowner do? Why?(C) Suppose the landowner is uncertain about the reliability of her geologist friend's estimate of the probability that oil will be found on her land. If she thinks the probability could be anywhere between 40% and 80%, would that change her decision?(D) Suppose that, in addition to the uncertainty about the probability of finding oil, the landowner is also uncertain about the cost of the exploratory well (could vary +/- 25%) and the future profits (could vary +/- 50%). To which of these variables is the expected value most sensitive?(E) What does the risk profile show about the relative risk levels for the landowner's two options?(F) Suppose the landowner suspects that she may be a somewhat risk-averse decision maker, because the she doesn"t feel there is as much of a difference between the two options as their expected values would indicate. She consults with a decision analysis expert who asks her to decide between two hypothetical alternatives: 1) a gamble with equal probabilities of winning an amount $X and losing an amount "$X/2, and 2) doing nothing, with a payoff of $0. The point at which she cannot decide between 1) and 2) is when X=$1,500,000. What is her risk tolerance if she uses an exponential utility function to model her preferences?(G) Apply the risk tolerance given in your answer to the previous question to the landowner's decision tree in (A). What is the optimal decision in this case? What is the resulting certainty equivalent?(H) If the landowner could hire an expert geologist prepare a report to help her make her decision, what is the most that information could be worth? Assume the geologist's information is perfectly reliable.
Q:
For a risk averse decision maker, the certainty equivalent is less than the expected monetary value (EMV).
Q:
The certainty equivalent is the certain dollar amount a risk-averse decision maker would accept in order to avoid a gamble altogether.
Q:
Utility function is a function that encodes a person's or company's feelings toward risk.
Q:
Rational decision makers are never willing to violate the expected monetary value (EMV) maximization criterion when large amounts of money are at stake.
Q:
Bayes' is useful in determining the value of perfect information (EVPI).