Suppose samples of size n = 16 are selected from a population with mean 80 and standard deviation 8. State the mean, standard error, and distribution of the sampling distribution of the sample mean.

(i) The mean is:

5.008 80cannot be determined.
(ii) The standard error is:0.802.00 8cannot be determined.
(iii) The shape of the distribution:
is normal because the population is normal. is approximately normal by the Central Limit Theorem. cannot be determined.

Step-by-step explanation:

(a)

(i)

The mean is 80

The mean of the sampling distribution of the mean will be the same as the mean of the population

(ii)

The standard error is

∅√n=8/√16 = 2

(iii) The shape of the distribution:

cannot be determined.

The sample size is too small to determine the shape of the distribution using CLT

(b)

(i)

The mean is 80

The mean of the sampling distribution of the mean will be the same as the mean of the population

(ii)

The standard error is

∅/√n=8/√100 = 0.8

(iii) The shape of the distribution:

is approximately normal by the Central Limit Theorem.

Since the sample size is 100, therefore we can approximate the distribution of the sample means as normal by CLT.

(c)

(i)

The mean is 80

The mean of the sampling distribution of the mean will be the same as the mean of the population

(ii)

The standard error is

∅/√n=8/√16 = 2

(iii) The distribution:

is normal because the population is normal