Question

Which of the following is true regarding the sampling distribution of the mean for a large sample size?

Select one:

a. It has the same shape, mean, and standard deviation as the population.

b. It has the same shape and mean as the population, but has a smaller standard deviation.

c. It has a normal distribution with the same mean as the population but with a smaller standard deviation.

d. It has a normal distribution with the same mean and standard deviation as the population.

Answer #1

according to central limit theorem, when the sample size is larger the sampling distribution of the sample mean tend to be normal with the same mean as the population , and the standard deviation as follows:

mean of sampling distribtion , where is population mean

standard deviation of sampling distribution =

so, correct answer is

**C:**

**It has a normal distribution with the same mean as the
population but with a smaller standard deviation**

Which of the following is NOT true regarding the sampling
distribution of the mean (Sample mean X-bar) for a large sample
size (sample size is greater than 36)? A. It has the same mean as
the population. B. It has a smaller standard deviation than the
population standard deviation. C. Approximately it follows a normal
distribution. D. It has the same distribution as the
population.

Question 2: Which of the following statements about the
sampling distribution of means is not true?
A. A sample distribution's mean will always equal the parent
population distribution's mean
B. The sampling distribution of means approximates the normal
curve.
C. The mean of a sampling distribution of means is equal to the
population mean.
D. The standard deviation of a sampling distribution of means is
smaller than the standard deviation of the population.

Which of the following statements is not true for sampling
distributions?
a. A sampling distribution is necessary for making confidence
statements about an unknown population parameter.
b. A sampling distribution depends on the nature of the
population being sampled.
c. When sampling at random from a normal population, the
sampling distribution for the sample average is a normal
distribution.
d. None of the above.
AND
TRUE or FALSE
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