 Quandaries and Queries

hi
name: fareeha
level: 12th
Student
My question has three parts to it and i don't understand how to do it.

Question:
A population consists of six numbers 1,2,3,4,5,6
a) How many different samples of two numbers can be selected with replacement? and list them.
b) Calculate the mean and standard deviation of the population
b2) Calculate the mean and standard deviation of the mean of the samples.
c) Find the standard error of your estimated mean in question b2 and compare with the estimated standard deviation in b2.

Thank you so much for helping me on this question. I will be waiting for the answer.

Hi Fareeha,

Use the expressions you know to calculate the mean and standard deviation of the six numbers 1,2,3,4,5,6. I want to call this standard deviation sigma so I can refer to it later.

You are to list all samples of size 2, selected with replacement. There are 6 ways to choose the first observation in each sample, and for each such choice there are 6 ways to select the second element. Thus there are 6 6 = 36 possible samples.

List all thirty-six samples and for each, calculate the mean.

sample mean
1,1 (1+1)/2 = 1
1,2 (1+2)/2 = 3/2
1,3 (1+3)/2 = 2
1,4 (1+4)/2 = 5/2
... ...

For b2) calculate the mean and standard deviation of the thirty-six items in the column labeled mean above.

Compare the standard deviation you just calculated to the quantity sigma/√n.

Penny   