LAB12 Instructions and Questions for Excel 2003
CONFIDENCE INTERVALS FOR POPULATION PROPORTION
NAME________________________LAB TIME_______LAB BLDG______________
1.
In this lab we will examine the procedure for estimation of the proportion of a population
which would favor a certain issue.
2.
To estimate the population proportion a random sample of people is selected and each
person is asked whether he/she supports the issue in question.
3.
The sample proportion, P-HAT, = number of “yes answers” / total number of answers.
4.
The formula for the Confidence Interval for the population proportion is:
P-HAT
+ / - Z* SQRT ( (P-HAT) (1 – P-HAT) / N )
5.
6.
PART A: SETTING UP YOUR SPREADSHEET
Use rows 2 and 3 for column headings as follows:
Column A:
Leave blank
Column B:
Sample size
Column C:
Confidence Level
Column D:
Z*
Column E:
P-HAT
Column F:
Margin Of Error
Column G:
Confidence Interval
Column H:
Leave Blank
Column I:
Interval Width
7.
Lets pretend that a sample of 1000 people is taken, and 500 people answer “yes”, and 500
people answer “no” on the issue in question.
Calculate a 95% Confidence Interval for the population proportion as follows:
In B5: enter 1000
In C5: enter .95 and format cell to display a percentage with 0 decimal places.
In D5: enter value of Z* for 95% confidence: 1.960
In E5: enter the value of P-HAT, 0.5
In F5: enter the formula: = D5*SQRT (E5* ( 1- E5) / B5)
In G5: enter the formula for the low limit: E5 – F5
In H5: enter the formula for the high limit: E5 + F5
In I5: enter the formula for the interval’s width: H5 – G5
8.
9.
For n = 1000, P-HAT = 0.5, the 95% Confidence Interval is __________________
10.
The margin of error in the above calculation is: _________________.
11.
PART B: EFFECT OF THE CONFIDENCE LEVEL ON THE MARGIN OF
ERROR AND THE WIDTH OF THE CONFIDENCE INTERVAL.
Enter 1000 in B8 through B12 to hold sample size constant at 1000.
Enter 0.5 in E8 through E12 to hold p-hat constant at 0.5
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
Enter the confidence levels given below in C8 through C12. Enter the corresponding
values of Z* in D8 through D12.
80%
1.282
90%
1.645
95%
1.960
99%
2.576
99.9%
3.291
Copy the formulas in F5 : I5 down to F8 : I8. The copy them down through line 12.
Use X/Y Scatterplot to plot the margin of error on Y axis vs confidence level on X
axis, and place the graph in the spreadsheet using the space J8:P23.
A 99% confidence interval for the population proportion would be wider ___ or narrower
____ than a 90% confidence interval.
PART C: EFFECT OF SAMPLE SIZE ON THE MARGIN OF ERROR AND THE
WIDTH OF THE CONFIDENCE INTERVAL.
In B25 through B29 enter the sample sizes 500, 1000, 2000, 4000 and 8000.
We will use 95% confidence with z = 1.96 and we will use P-HAT = 0.5. Enter these
values in C25, D25 and E25 and then copy them down through line 29.
Copy the formulas from F12:I12 to F25:I25. Then copy them down through line 29.
Use X/Y scatterplot to plot the margin of error (y axis) vs the sample size (x axis),
and place the graph in the spreadsheet using the space J25:P39.
As the sample size increases, the margin of error and the width of the confidence interval:
1)
Increases _________
2)
Decreases _________
To cut the margin of error in half, the sample size must be _______________ by a factor
of _____________.
PART D: EFFECT OF THE PROPORTION ON THE MARGIN OF ERROR
AND THE WIDTH OF THE CONFIDENCE INTERVAL.
We will hold the sample size constant at 1000, and the confidence level constant at 95%.
Enter 1000 in B41, 95% in C41, 1.96 in D41, and copy these values down through line
53.
In Column E on lines 41 through 53 enter the following values of P-HAT:
.005
.05
.1
.2
.3
.4
.5
.6
.7
.8
.9
.95
.995
Copy the formulas in F29:I29 and paste them in F41:I41. Then copy them down through
line 53.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
Use X/Y Scatterplot to plot the margin of error (y axis) vs P-HAT (x axis) and put
the graph in the spreadsheet using the space J41:P57.
What value of the proportion produces the maximum margin of error?________
PART E: EFFECT OF THE PROPORTION ON THE SAMPLE SIZE
REQUIRED TO OBTAIN A DESIRED MARGIN OF ERROR.
In C59 enter 95% and in D59 enter 1.96. Enter .03 in F59. Then copy these values down
through line 71.
Enter the following values for the proportion in Column E, lines 59-71:
.005
.05
.10
.20
.30
.40
.50
.60
.70
.80
.90
.95
.995
In B59 enter the formula to calculate the sample size :
= E59*(1-E59)* (D59 / F59 ) ^2
Copy the formula in B59 down through B71.
Use X/Y scatterplot to plot the sample size ( y axis ) vs the proportion ( x axis), and
put the graph in the spreadsheet using the space J59:P71.
Print the spreadsheet from A1 to P71 on one page and turn in with your answers.
The spreadsheet should have four graphs on it.
What value of the proportion requires the largest sample size in order to maintain
a margin of error of .03? ______________________