Question

Which of the following statements are true? I. The sampling distribution of x? has standard deviation ?/?n even if the population is not normally distributed. II. The sampling distribution of x? is normal if the population has a normal distribution. III. When n is large, the sampling distribution of x? is approximately normal even if the the population is not normally distributed. I and II I and III II and III I, II, and III None of the above gives the complete set of true responses.

          Which of the following statements are true?

I. The sampling distribution of x? has standard deviation ?/?n even if the population is not normally distributed.
II. The sampling distribution of x? is normal if the population has a normal distribution.
III. When n is large, the sampling distribution of x? is approximately normal even if the the population is not normally distributed.

I and II
I and III
II and III
I, II, and III
None of the above gives the complete set of true responses.

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Which of the following statements are true?

I. The sampling distribution of x? has standard deviation ?/?n even if the population is not normally distributed.
II. The sampling distribution of x? is normal if the population has a normal distribution.
III. When n is large, the sampling distribution of x? is approximately normal even if the the population is not normally distributed.

I and II
I and III
II and III
I, II, and III
None of the above gives the complete set of true responses.

Added by Tracy B.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Madhur L

08/01/2023

Step 1

The sampling distribution of z has a standard deviation even if the population is not normally distributed. This statement is true. The z-score is calculated as (sample mean - population mean) / (population standard deviation / sqrt(n)). The standard deviation of Show more…

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Which of the following statements are true? I. The sampling distribution of x̄ has standard deviation σ/√n even if the population is not normally distributed. II. The sampling distribution of x̄ is normal if the population has a normal distribution. III. When n is large, the sampling distribution of x̄ is approximately normal even if the population is not normally distributed. I and II I and III II and III I, II, and III None of the above gives the complete set of true responses.

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