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StatTutor Lesson - Sampling Distribution of ¯x

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      Question 1

      62

      Question 1.

      What characteristics of the sampling distribution of ¯x are we interested in?

      A.
      B.

      Correct. For all histograms, we investigate shape, center and spread. The sampling distribution of ¯x’s is no different.
      Incorrect. For all histograms, we investigate shape, center and spread. The sampling distribution of ¯x’s is no different.
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      Questions 2-3

      132

      Question 2.

      What is the mean of the sampling distribution of ¯x?

      A.
      B.
      C.

      Correct. The mean of the sampling distribution of ¯x always equals the mean of the population, μ.
      Incorrect. The mean of the sampling distribution of ¯x always equals the mean of the population, μ.
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      Questions 4-5

      245

      Question 4.

      What is the standard deviation of the sampling distribution of ¯x?

      A.
      B.
      C.
      D.

      Correct. The standard deviation of the sampling distribution of ¯x equals the standard deviation of the population, σ, divided by the square root of sample size: σn
      Incorrect. The standard deviation of the sampling distribution of ¯x equals the standard deviation of the population, σ, divided by the square root of sample size: σn
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      Questions 6-7

      305

      Question 6.

      True or false: The shape of the sampling distribution of ¯x is always Normal when the shape of the population is Normal regardless of sample size.

      A.
      B.

      Correct. This statement gives case 1: The shape of the sampling distribution of ¯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 ¯x is Normal when the shape of the population is Normal for any n.
      2
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      Question 8

      379

      Question 8.

      If the population has a Normal shape, when should we compute probabilities on ¯x?

      A.
      B.
      C.

      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.
      2
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      Questions 9-12

      502

      Question 9.

      True or false: The mean of the sampling distribution of ¯x always exactly equals μ.

      A.
      B.

      Correct. This is a correct statement.
      Incorrect. This is a correct statement.
      2
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