Statistics

These are the questions, along with the answer to the questions. How do I solve this using a calculator? Step by step?

Assume a population of 6, 4 and 9. Assume that samples of size n=2 are randomly selected with replacement from the population. Listed below are the nine different samples. Complete parts a through d below.

6,6    6,4    6,9    4,6    4,4    4,9    9,6    9,4    9,9

1. Find the value of the population standard deviation Q

    

   First calculate the population mean, rounding to two decimals places.

µ=

= 6.33

= 2.055

1. Find the standard deviation of each of the nine samples, then summarize the sampling distribution of the standard deviations in the format of a table representing the probability distribution. Begin by finding all sample standard deviations.

2. While either technology or the formula below can be used to find each sample standard deviation, where X is the sample mean and N is the sample size, for the exercise, use the following formula.

First, calculate the sample standard deviation for 6.6. Determine X by substituting the values and simplifying.

X=

=  = 6

Now solve for s. Substitute x=6 and the sample values 6 and 6 for x into the sample standard deviation formula to solve for s.

 =0

Use a similar process to find the sample standard deviations for the other samples. Note that the probability of each sample is 1/9 because each of the nine samples are equally likely.

Now, summarize the sampling distribution of the standard deviations in the format of a table representing the probability distribution. Because each sample is equally likely to occur, the probability of a certain standard value is the number of occurrences of that standard deviation value divided by the total number of samples, 9.

1. Find the mean of the sampling distribution of the sample standard deviation. The mean of the sample standard deviation is the sum of the nine-sample standard deviation divided by the number of samples.

2. Calculate the mean of the sample standard deviation, rounded to three decimal places.

d. Do the sample standard deviation target the value of the population standard deviation? In general, do sample standard deviations make good estimators of population standard deviations? Why or why not?