# Chapter 1. Sampling Distribution of $$\overline{x}$$

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1:02

### Question 1.1

Correct. For all histograms, we investigate shape, center and spread. The sampling distribution of $$\overline{x}$$’s is no different.
Incorrect. For all histograms, we investigate shape, center and spread. The sampling distribution of $$\overline{x}$$’s is no different.
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2:12

### Question 1.2

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Correct. The mean of the sampling distribution of $$\overline{x}$$ always equals the mean of the population, μ.
Incorrect. The mean of the sampling distribution of $$\overline{x}$$ always equals the mean of the population, μ.
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### Question 1.3

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Correct. The mean of the sampling distribution of $$\overline{x}$$ always equals the mean of the population regardless of sample size or population shape.
Incorrect. The mean of the sampling distribution of $$\overline{x}$$ always equals the mean of the population regardless of sample size or population shape.
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4:05

### Question 1.4

Correct. The standard deviation of the sampling distribution of $$\overline{x}$$ equals the standard deviation of the population, σ, divided by the square root of sample size: $$\frac{ \sigma }{ \sqrt{n} }$$
Incorrect. The standard deviation of the sampling distribution of $$\overline{x}$$ equals the standard deviation of the population, σ, divided by the square root of sample size: $$\frac{ \sigma }{ \sqrt{n} }$$
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### Question 1.5

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Correct. For the formula to be valid, the sample must be SRS. Otherwise, the standard deviation of the sampling distribution of $$\overline{x}$$ equals $$\frac{ \sigma }{ \sqrt{n} }$$ regardless of the sample size and shape of the population.
Incorrect. For the formula to be valid, the sample must be SRS. Otherwise, the standard deviation of the sampling distribution of $$\overline{x}$$ equals $$\frac{ \sigma }{ \sqrt{n} }$$ regardless of the sample size and shape of the population.
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5:05

### Question 1.6

Correct. This statement gives case 1: The shape of the sampling distribution of $$\overline{x}$$ is Normal when the shape of the population is Normal for any n.
Incorrect. This statement gives case 1: The shape of the sampling distribution of $$\overline{x}$$ is Normal when the shape of the population is Normal for any n.
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### Question 1.7

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Correct. The shape of the sampling distribution of $$\overline{x}$$ is Normal IF (case 1) the population is Normal or (case 2) the sample size is large provided the samples are SRS. Thus, if the population shape is non-Normal, the shape of the sampling distribution of $$\overline{x}$$ is approximately Normal if the sample size is large.
Incorrect. The shape of the sampling distribution of $$\overline{x}$$ is Normal IF (case 1) the population is Normal or (case 2) the sample size is large provided the samples are SRS. Thus, if the population shape is non-Normal, the shape of the sampling distribution of $$\overline{x}$$ is approximately Normal if the sample size is large.
2
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6:19

### Question 1.8

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Correct. If an SRS is not taken, the sample results will be biased and the probability computed will not be correct.
Incorrect. If an SRS is not taken, the sample results will be biased and the probability computed will not be correct.
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8:22

### Question 1.9

Correct. This is a correct statement.
Incorrect. This is a correct statement.
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### Question 1.10

Correct. This is a correct statement.
Incorrect. This is a correct statement.
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### Question 1.11

Correct. If the population shape is Normal, the shape of the sampling distribution of $$\overline{x}$$ will be Normal regardless of sample size.
Incorrect. If the population shape is Normal, the shape of the sampling distribution of $$\overline{x}$$ will be Normal regardless of sample size.