SOCSCI
101 EXERCISE FOR ESTIMATING THE POPULATION MEAN
AND
DETERMINING SAMPLE SIZE
INTRODUCTION
This exercise will require you to be creative and do
experiments on Excel (you will be lost but that is part of my design for this
exercise because in being lost you will learn a number of things). Our class is not an Excel computer class
and, thus, Excel will not be taught. Excel is user-friendly enough to be
self-studied through experimentation and through its help command. In using Excel’s help command, I strongly
recommend that you CLICK HELP, THEN CLICK CONTENT AND INDEX, GO TO INDEX AND
TYPE “STATISTICAL FUNCTIONS,” AND LOOK FOR THE FUNCTION IN THE STATISTICAL
FUNCTION MENU. Utilizing Excel’s search function may not lead to more
satisfactory results.
Your God-given talents and intelligence will see you
through. Learning from your classmates is allowed but copying his or her work
is not allowed. To a certain extent I will be able to detect copying of works
among you.
I.
EXERCISE
PROPER: USE EXCEL COMMANDS DESCRIBED IN II BELOW TO CREATE THE FOLLOWING EXCEL
PROGRAMS
1.
ESTIMATE
THE POPULATION MEAN WHEN THE SAMPLE SIZE IS n>30 AT THE 95% CONFIDENCE
LEVEL, SAMPLE MEAN, AND SAMPLE STANDARD DEVIATION. IN THIS PROGRAM, MAKE THE
NECESSARY INTRODUCTION AND INSTRUCT USERS TO ENTER THE SAMPLE MEAN, SAMPLE
STANDARD DEVIATION, AND SAMPLE SIZE AT PRE-IDENTIFIED CELLS.
2.
ESTIMATE
THE POPULATION MEAN WHEN THE SAMPLE SIZE IS n<30 AT THE 95% CONFIDENCE LEVEL
GIVEN SAMPLE SIZE (AND THEREFORE DEGREES OF FREEDOM) AND SAMPLE STANDARD
DEVIATION. IN THIS PROGRAM, MAKE THE NECESSARY INTRODUCTION AND INSTRUCT USERS
TO ENTER THE SAMPLE MEAN, SAMPLE STANDARD DEVIATION, AND SAMPLE SIZE AT
PRE-IDENTIFIED CELLS.
3.
ESTIMATE
THE POPULATION PROPORTION AT THE 95% CONFIDENCE LEVEL AND SAMPLE PROPORTION
PROVIDED THE SAMPLE IS LARGE ENOUGH (OR THAT n*p hat or n*q hat is at least
five) AND WHEN THERE IS A PRELIMINARY SAMPLE.
IN THIS PROGRAM, MAKE THE NECESSARY INTRODUCTION AND THEN INSTRUCT USERS
TO ENTER SAMPLE PROPORTION AND SAMPLE SIZE.
II.
HERE
ARE THE EXCEL COMMANDS USEFUL FOR THE EXERCISE ABOVE (AGAIN, FOR DETAILS, CLICK HELP, THEN CLICK CONTENT AND INDEX, GO
TO INDEX AND TYPE “STATISTICAL FUNCTIONS,” AND LOOK FOR THE FUNCTION IN THE
STATISTICAL FUNCTION MENU)
1. USING NORMSINV
This gives us the Z value associated with a probability from minus infinity of Z to the said Z.
Syntax: @normsinv(probability)
Probability is a probability corresponding to the normal distribution.
· If probability is nonnumeric, NORMSINV returns the #VALUE! error value.
· If probability < 0 or if probability > 1, NORMSINV returns the #NUM! error value.
NORMSINV uses an iterative technique for calculating the function. Given a probability value, NORMSINV iterates until the result is accurate to within ± 3x10^-7. If NORMSINV does not converge after 100 iterations, the function returns the #N/A error value.
For a 95% confidence level, you would use the probability levels 97.5% and 2.5%.
2. USING TINV
Returns the inverse of the Student's t-distribution for the
specified degrees of freedom.
Syntax:: @tinv(probability,degrees of freedom)
Probability is the alpha in the Student's t-distribution. For a 95% confidence level, the probability to use is 0.05.
Degrees_freedom is the number of degrees of freedom to characterize the distribution.
Remarks
· If either argument is nonnumeric, TINV returns the #VALUE! error value.
· If probability < 0 or if probability > 1, TINV returns the #NUM! error value.
· If degrees_freedom is not an integer, it is truncated.
· If degrees_freedom < 1, TINV returns the #NUM! error value.
· TINV is calculated as TINV = p( t<X ), where X is a random variable that follows the t-distribution.
TINV uses an iterative technique for calculating the function. Given a probability value, TINV iterates until the result is accurate to within ± 3x10^-7. If TINV does not converge after 100 iterations, the function returns the #N/A error value.
Example: @tinv(0.054645,60) equals 1.96
III. BASIC FORMAT FOR EACH EXCEL PROGRAM
1. PROGRAM FOR _______
INTRODUCTION
INSTRUCTIONS
PLEASE ENTER ________: ________
PLEASE ENTER ________:
THE ESTIMATE FOR ___ IS _____<____< _____
2. PROGRAM FOR ______
IV. WHEN YOU HAVE FINISHED THE ABOVE, I MAY ASK YOU TO DO A SIMILAR PROGRAM FOR ESTIMATING THE MINIMUM SIZE OF RANDOM SAMPLE WHICH IS TOPIC 10 OF THE SYLLABUS.