Chapter 1. Sampling Distributions

Correct. This is a correct statement.

Incorrect. This is a correct statement.

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Correct. We generally need a minimum of 2000 samples.

Incorrect. We generally need a minimum of 2000 samples.

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Correct. To investigate the behavior of \(\overline{x} \), we need to have many \(\overline{x} \)’s which we get from taking many, many samples and computing \(\overline{x} \) for each.

Incorrect. To investigate the behavior of \(\overline{x} \), we need to have many \(\overline{x} \)’s which we get from taking many, many samples and computing \(\overline{x} \) for each.

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Correct. In order to do inference, we must know about the behavior of \(\overline{x} \) and so we must study its behavior with the sampling distribution of \(\overline{x} \).

Incorrect. In order to do inference, we must know about the behavior of \(\overline{x} \) and so we must study its behavior with the sampling distribution of \(\overline{x} \).

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Correct. Even though it is called the “sampling distribution of \(\overline{x} \)," it is the distribution of all \(\overline{x} \)’s from all possible samples.

Incorrect. Even though it is called the “sampling distribution of \(\overline{x} \)," it is the distribution of all \(\overline{x} \)’s from all possible samples.

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Correct. The sampling distribution of \(\overline{x} \) is the collection (distribution) of \(\overline{x} \)-values from all possible samples of the same size from the same population.

Incorrect. The sampling distribution of \(\overline{x} \) is the collection (distribution) of \(\overline{x} \)-values from all possible samples of the same size from the same population.

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Correct. We actually need fewer samples and we don’t have to list all possible samples. Taking two thousand samples is usually enough to get a good estimation of the actual sampling distribution of \(\overline{x} \).

Incorrect. We actually need fewer samples and we don’t have to list all possible samples. Taking two thousand samples is usually enough to get a good estimation of the actual sampling distribution of \(\overline{x} \).

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Correct. The mean of all the individuals in the population is the parameter. In this case, all individuals are all stocks on the New York stock exchange. The measurement on each stock is the closing price. So the parameter in context is the mean closing price of all New York Stock Exchange stocks.

Incorrect. The mean of all the individuals in the population is the parameter. In this case, all individuals are all stocks on the New York stock exchange. The measurement on each stock is the closing price. So the parameter in context is the mean closing price of all New York Stock Exchange stocks.

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Correct. Don’t confuse the sample size with the number of samples we are going to take. We need to take many, many samples of size 4 and find the mean of the four prices for each sample of size four.

Incorrect. Don’t confuse the sample size with the number of samples we are going to take. We need to take many, many samples of size 4 and find the mean of the four prices for each sample of size four.

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Correct. For all histograms, we investigate shape, center and spread. This histogram of \(\overline{x} \)’s is no different.

Incorrect. For all histograms, we investigate shape, center and spread. This histogram of \(\overline{x} \)’s is no different.

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Correct. One sample mean is not a sampling distribution of \(\overline{x} \); we need all possible \(\overline{x} \)’s for the sampling distribution of \(\overline{x} \).

Incorrect. One sample mean is not a sampling distribution of \(\overline{x} \); we need all possible \(\overline{x} \)’s for the sampling distribution of \(\overline{x} \).

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Correct. \(\overline{x} \)-values from many many samples estimate the sampling distribution of \(\overline{x} \).

Incorrect. \(\overline{x} \)-values from many many samples estimate the sampling distribution of \(\overline{x} \).

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Correct. Since we are constructing a histogram of \(\overline{x} \)’s, each circle represents the value of one \(\overline{x} \).

Incorrect. Since we are constructing a histogram of \(\overline{x} \)’s, each circle represents the value of one \(\overline{x} \).

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Correct. Since the histogram displays \(\overline{x} \)’s, it displays the estimated sampling distribution of \(\overline{x} \).

Incorrect. Since the histogram displays \(\overline{x} \)’s, it displays the estimated sampling distribution of \(\overline{x} \).

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Correct. The mean of the sampling distribution of \(\overline{x} \) we need all possible \(\overline{x} \) equals the mean of the population.

Incorrect. The mean of the sampling distribution of \(\overline{x} \) we need all possible \(\overline{x} \) equals the mean of the population.

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Correct. Sample means are typically closer to μ than measurements on individuals. Thus, sample means (displayed in the red histogram on the right) are less variable than individual measurements (displayed in the blue histogram on the left).

Incorrect. Sample means are typically closer to μ than measurements on individuals. Thus, sample means (displayed in the red histogram on the right) are less variable than individual measurements (displayed in the blue histogram on the left).

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Correct. Averaging the sample means tends to average out the skewness. The bigger the sample size, the more skewness is averaged out and the more symmetrically the sample means cluster about μ.

Incorrect. Averaging the sample means tends to average out the skewness. The bigger the sample size, the more skewness is averaged out and the more symmetrically the sample means cluster about μ.

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Correct.

Incorrect.

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Correct.

Incorrect.

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Correct.

Incorrect.

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Correct. The mean of the sampling distribution of \(\overline{x} \) equals the mean of the population.

Incorrect. The mean of the sampling distribution of \(\overline{x} \) equals the mean of the population.

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Correct. Sample means are typically closer to μ than measurements on individuals. Thus, as with samples of size 4, sample means (displayed in the red histogram on the right) are less variable than individual measurements (displayed in the blue histogram on the left).

Incorrect. Sample means are typically closer to μ than measurements on individuals. Thus, as with samples of size 4, sample means (displayed in the red histogram on the right) are less variable than individual measurements (displayed in the blue histogram on the left).

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Correct. The averaging process used to compute sample means tends to average out skewness. The bigger the sample size, the more skewness is averaged out and the more symmetrically the sample means cluster about μ. Thus, the histogram of sample means from samples of size 16 is closer to Normal in shape than the histogram of closing stock prices.

Incorrect. The averaging process used to compute sample means tends to average out skewness. The bigger the sample size, the more skewness is averaged out and the more symmetrically the sample means cluster about μ. Thus, the histogram of sample means from samples of size 16 is closer to Normal in shape than the histogram of closing stock prices.

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Correct. Since the mean of the sampling distribution of \(\overline{x} \) equals the mean of the population, the means of all sampling distributions are equal.

Incorrect. Since the mean of the sampling distribution of \(\overline{x} \) equals the mean of the population, the means of all sampling distributions are equal.

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Correct. Since the larger the sample size, the closer the sample means are to µ, sample means from larger samples have less spread than sample means from smaller samples.

Incorrect. Since the larger the sample size, the closer the sample means are to µ, sample means from larger samples have less spread than sample means from smaller samples.

2

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Correct. The averaging process used to compute sample means tends to average out skewness. The bigger the sample size, the more skewness is averaged out and the more symmetrically the sample means cluster about μ. The histogram of sample means from samples of size 16 is closer to Normal in shape than the histogram of sample means from samples of size 4.

Incorrect. The averaging process used to compute sample means tends to average out skewness. The bigger the sample size, the more skewness is averaged out and the more symmetrically the sample means cluster about μ. The histogram of sample means from samples of size 16 is closer to Normal in shape than the histogram of sample means from samples of size 4.

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Correct. The mean of the sampling distribution of \(\overline{x} \) equals the mean of the population which is 26.

Incorrect. The mean of the sampling distribution of \(\overline{x} \) equals the mean of the population which is 26.

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Correct. Since the larger the sample size, the closer the sample means are to µ, sample means from larger samples have less spread than sample means from smaller samples. So, as sample size increases the spread of the sampling distribution of \(\overline{x} \) decreases.

Incorrect. Since the larger the sample size, the closer the sample means are to µ, sample means from larger samples have less spread than sample means from smaller samples. So, as sample size increases the spread of the sampling distribution of \(\overline{x} \) decreases.

2

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Correct. The averaging process used to compute sample means tends to average out skewness. The bigger the sample size, the more skewness is averaged out and the more symmetrically the sample means cluster about μ. So, as sample size increases, the shape of the sampling distribution of \(\overline{x} \) gets more Normal.

Incorrect. The averaging process used to compute sample means tends to average out skewness. The bigger the sample size, the more skewness is averaged out and the more symmetrically the sample means cluster about μ. So, as sample size increases, the shape of the sampling distribution of \(\overline{x} \) gets more Normal.

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Correct. Since the shape of the sampling distribution of \(\overline{x} \) is approximately Normal for large sample sizes, we will take a large sample and use a Normal curve.

Incorrect. Since the shape of the sampling distribution of \(\overline{x} \) is approximately Normal for large sample sizes, we will take a large sample and use a Normal curve.

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