Problem 1 In a small company there are ten staff member work

Problem 1. In a small company, there are ten staff member working (N=10). Their annual salaries (unit: $1,000) are

Population:11.6, 10.7, 7.2, 3.5, 9.8, 7.0, 11.8, 11.5, 15.1, 11.8

a. If you want to randomly sample two staff members and inquire of their salaries, find out how many different ways you can choose two people out of ten people with replacement.

b. Write down all possible samples of size 2 drawn with replacement (Example, {11.6, 10.7}, {11.6 7.2}, ...)

c. Compute the mean of each sample of size 2 (you should have many different means for this question).

d. Make a histogram (sampling distribution) with the computed means.

e. Compute the mean of the means of all samples of size 2.

f. Compute the standard deviation of the means of all samples of size 2.

g. Compute the answer for (f) by using the equation of /n , where =population standard deviation, and

n=sample size.

h. Why do you think that the answers from (f) and (g) show discrepancy slightly?

Solution

1) No of staff members = 10

a) No of ways to select 2 staff members with replacement = 10 * 10 = 100

b) samples: {11.6,11.6}; {11.6,10.7}; {11.6,7.2}; {11.6,3.5}; {11.6,9.8}; {11.6,7.0}; {11.6,11.8}; {11.6,11.5}; {11.6,15.1};{11.6,11.8}

{10.7,11.6}; {10.7,10.7}; {10.7,7.2}; {10.7,3.5}; {10.7,9.8}; {10.7,7.0}; {10.7,11.8}; {10.7,11.5}; {10.7,15.1};{10.7,11.8}

{7.2,11.6}; {7.2,10.7}; {7.2,7.2}; {7.2,3.5}; {7.2,9.8}; {7.2,7.0}; {7.2,11.8}; {7.2,11.5}; {7.2,15.1};{7.2,11.8}

{3.5,11.6}; {3.5,10.7}; {3.5,7.2}; {3.5,3.5}; {3.5,9.8}; {3.5,7.0}; {3.5,11.8}; {3.5,11.5}; {3.5,15.1};{3.5,11.8}

{9.8,11.6}; {9.8,10.7}; {9.8,7.2}; {9.8,3.5}; {9.8,9.8}; {9.8,7.0}; {9.8,11.8}; {9.8,11.5}; {9.8,15.1};{9.8,11.8}

{7,11.6}; {7,10.7}; {7,7.2}; {7,3.5}; {7,9.8}; {7,7.0}; {7,11.8}; {7,11.5}; {7,15.1};{7,11.8}

{11.8,11.6}; {11.8,10.7}; {11.8,7.2}; {11.8,3.5}; {11.8,9.8}; {11.8,7.0}; {11.8,11.8}; {11.8,11.5}; {11.8,15.1};{11.8,11.8}

{11.5,11.6}; {11.5,10.7}; {11.5,7.2}; {11.5,3.5}; {11.5,9.8}; {11.5,7.0}; {11.5,11.8}; {11.5,11.5}; {11.5,15.1};{11.5,11.8}

{15.1,11.6}; {15.1,10.7}; {15.1,7.2}; {15.1,3.5}; {15.1,9.8}; {15.1,7.0}; {15.1,11.8}; {15.1,11.5}; {15.1,15.1};{15.1,11.8}

{11.8,11.6}; {11.8,10.7}; {11.8,7.2}; {11.8,3.5}; {11.8,9.8}; {11.8,7.0}; {11.8,11.8}; {11.8,11.5}; {11.8,15.1};{11.8,11.8}

c) Means in the respective order are as follows:

e) Mean of all means = 4.314

f) stdev = 4.297

g) population stdev = 6.75 (Use STDEV function)

h) beacuse the margin of error reduces when we calculate means