Reading 10: Sampling and Estimation LOS a习题精选 error, simple, interpret, class, div

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Session 3: Quantitative Methods: Application
Reading 10: Sampling and Estimation

LOS a: Define simple random sampling, sampling error, and a sampling distribution, and interpret sampling error.

Sampling error can be defined as:

A) the standard deviation of a sampling distribution of the sample means.

B) the difference between a sample statistic and its corresponding population parameter.

C) rejecting the null hypothesis when it is true.

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This is the definition.

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The sampling distribution of a statistic is:

A) always a standard normal distribution.

B) the probability distribution consisting of all possible sample statistics computed from samples of the same size drawn from the same population.

C) the same as the probability distribution of the underlying population.

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A sample statistic itself is a random variable, so it also has a probability distribution. For example, suppose we start with a sample of the prices of 200 stocks, and we calculate the sample mean of a random sample of 40 of those stocks. If we repeat this many times, we will have many different estimates of the sample mean. The distribution of these estimates of the mean is the sampling distribution of the mean. A statistic’s sampling distribution is not necessarily normal or the same as that of the population.

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A sample of five numbers drawn from a population is (5, 2, 4, 5, 4). Which of the following statements concerning this sample is most accurate?

A) The mean of the sample is ∑X / (n ? 1) = 5.

B) The variance of the sample is: ∑(x1 ? mean of the sample)2 / (n ? 1) = 1.5.

C) The sampling error of the sample is equal to the standard error of the sample.

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The mean of the sample is ∑X / n = 20 / 5 = 4. The sampling error of the sample is the difference between a sample statistic and its corresponding population parameter.

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An analyst wants to generate a simple random sample of 500 stocks from all 10,000 stocks traded on the New York Stock Exchange, the American Stock Exchange, and NASDAQ. Which of the following methods is least likely to generate a random sample?

A) Assigning each stock a unique number and generating a number using a random number generator. Then selecting the stock with that number for the sample and repeating until there are 500 stocks in the sample.

B) Listing all the stocks traded on all three exchanges in alphabetical order and selecting every 20th stock.

C) Using the 500 stocks in the S& 500.

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The S& 500 is not a random sample of all stocks traded in the U.S. because it represents the 500 largest stocks. The other two choices are legitimate methods of selecting a simple random sample.

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Which of the following statements about sampling errors is least accurate?

A) Sampling error is the difference between a sample statistic and its corresponding population parameter.

B) Sampling errors are errors due to the wrong sample being selected from the population.

C) Sampling error is the error made in estimating the population mean based on a sample mean.

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Sampling error is the difference between a sample statistic (the mean, variance, or standard deviation of the sample) and its corresponding population parameter (the mean, variance, or standard deviation of the population).

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A simple random sample is a sample constructed so that:

A) the sample size is random.

B) each element of the population is also an element of the sample.

C) each element of the population has the same probability of being selected as part of the sample.

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Simple random sampling is a method of selecting a sample in such a way that each item or person in the population being studied has the same (non-zero) likelihood of being included in the sample.

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Sampling error is the:

A) difference between a sample statistic and its corresponding population parameter.

B) estimation error created by using a non-random sample.

C) difference between the point estimate of the mean and the mean of the sampling distribution.

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Sampling error is the difference between any sample statistic (the mean, variance, or standard deviation of the sample) and its corresponding population parameter (the mean, variance or standard deviation of the population). For example, the sampling error for the mean is equal to the sample mean minus the population mean.

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From the entire population of McDonald’s franchises, an analyst constructs a sample of the monthly sales volume for 20 randomly selected franchises. She calculates the mean sales volume for those 20 franchises to be $400,000. The sampling distribution of the mean is the probability distribution of the:

A) mean monthly sales volume estimates from all possible samples of 20 observations.

B) mean monthly sales volume estimates from all possible samples.

C) monthly sales volume for all McDonald’s franchises.

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The sampling distribution of a sample statistic is a probability distribution made up of all possible sample statistics computed from samples of the same size randomly drawn from the same population, along with their associated probabilities.

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Which of the following statements about confidence intervals is least accurate? A confidence interval:

A) expands as the probability that a point estimate falls within the interval decreases.

B) has a significance level that is equal to one minus the degree of confidence.

C) is constructed by adding and subtracting a given amount from a point estimate.

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A confidence interval contracts as the probability that a point estimate falls within the interval decreases.

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An investment has a mean return of 15% and a standard deviation of returns equal to 10%. Which of the following statements is least accurate? The probability of obtaining a return:

A) between 5% and 25% is 0.68.

B) greater than 25% is 0.32.

C) greater than 35% is 0.025.

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Sixty-eight percent of all observations fall within +/- one standard deviation of the mean of a normal distribution. Given a mean of 15 and a standard deviation of 10, the probability of having an actual observation fall within one standard deviation, between 5 and 25, is 68%. The probability of an observation greater than 25 is half of the remaining 32%, or 16%. This is the same probability as an observation less than 5. Because 95% of all observations will fall within 20 of the mean, the probability of an actual observation being greater than 35 is half of the remaining 5%, or 2.5%.