Population Parameters Use the same population of {4, 5, 9} from Example 1 in Section 6-4. Assume that samples of size n = 2 are randomly selected without replacement.

a. Find μ and σ for the population.

b. After finding all samples of size n = 2 that can be obtained without replacement, find the population of all values of by finding the mean of each sample of size n = 2.

c. Find the mean and standard deviation for the population of sample means found in part (b).

d. Verify that

Example 1 Normal, Uniform, and U-Shaped Distributions

Solution 25BB

The value 4, 5, 9 are considered a population, the population mean is 6.The mean for the population of sample means found in part (b) is 1.08.

b)

After finding all samples of size that can be obtained without replacement, the population of all x values of by the finding the mean of each sample of size is:

We have to become table for without replacement sample mean and standard deviation is:

...Sample | Sample mean | ||

4,5 | 4.5 | -1.5 | 2.25 |

4,9 | 6.5 | 0.5 | 0.25 |

5,4 | 4.5 | -1.5 | 2.25 |

5,9 | 7 | 1 |