Download Lab 9 instructions and questions for Excel 2003 DUE ON NOV 10.

LAB 9 INSTRUCTIONS FOR EXCEL 2003
CONFIDENCE INTERVAL FOR THE POPULATION MEAN
NAME____________________________LAB TIME_______LAB BLDG_________
In this lab we will examine how confidence intervals for the population mean are
calculated, how often they are correct, and the factors that affect the interval’s width.
GENERATE 100 RANDOM SAMPLES OF SIZE=20, AND CALCULATE A 95%
CONFIDENCE INTERVAL BASED ON EACH SAMPLE.
1.
Open an Excel file.
2.
Do Tools>Data Analysis>Random Number Generation>OK
3.
Number of variables = 20; Number of Random Numbers = 100;
4.
Distribution = Normal; Mean = 10000; Std Dev = 1000
5.
Skip Random Seed: Click on Output Range; Enter A2 in window
6.
Go back to Random Seed and enter 16892; Click OK
7.
You should get random numbers in A2:T101.
8.
In V1 enter Sample Mean: In W1 enter Lower Confidence Limit; In X1 enter
Upper Confidence Limit; In Z1 enter 0=true, 1=false
9.
In V2 calculate the mean for A2:T2
10.
In W2 calculate the lower confidence limit: =V2 - 1.96 * 1000/sqrt(20)
11.
In X2 calculate the upper confidence limit: =V2 + 1.96 * 1000/sqrt(20)
12.
In Z2 enter logic to determine whether each interval includes the true population
mean of 10000: =, get the IF function, get the window and for Logical Test use
W2<10000, Go down to Value if false: 1, Go up to Value if true: get another IF
function by clicking on IF in the tool bar at the left edge. In the new window:
Logical Test: use X2>10000, Value if true: 0, Value if false: 1 Click OK. You
should get a 0 since the interval on line 2 does include 10000.
13.
Copy the formulas in V2:Z2 down through line 101.
14.
In Z104 calculate the sum for Z2:Z101. This gives the number of intervals which
were incorrect out of the 100 applications of the confidence interval formula.
Number of intervals incorrect= _______, number correct = _________
EXAMINE THE EFFECT OF SAMPLE SIZE AND CONFIDENCE LEVEL ON THE
WIDTH OF THE CONFIDENCE INTERVAL.
15.
To examine the effect of sample size on the width of a confidence interval, three
samples of size n=20, n=80 and n=320 are to be taken from a population. Lets
pretend that from previous studies we know the standard deviation of the
population, σ = 1000.
16.
Lets also pretend that the mean for each sample = 10000. We are just doing this
to simplify the calculations. The actual sample means do not matter when we are
calculating the width of the confidence interval
17.
Using the formula for the confidence interval, calculate nine intervals, using
sample sizes of 20, 80 and 320 and confidence levels of 90%, 95% and 99%. You
can set this up in excel as follows:
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
On line 110, in col B enter “conf level”, in col C enter “z*” , in col D
enter “sample size” , in col E enter “sample mean”, in col F enter “lower
conf limit”, in col G enter “upper conf limit”, in col H enter “width”
On line 111, in col B enter 90%, in col C enter 1.645, in col D enter 20,
in col E enter 10000.
In F111 enter =E111-C111*1000/SQRT(D111) to calculate Lower
Confidence Limit.
In G111 enter =E111 +C111*1000/SQRT(D111) to calculate Upper
Confidence Limit.
In H111 enter = G111-F111 to calculate Width of Confidence Interval.
On line 112 copy line 111 down and then change the sample size in col D
to 80,
On line 113, copy line 112 down and then change the sample size in col D
to 320.
Set up lines 114, 115 and 116 to be the same as lines 111, 112 and 113
except use a confidence of 95% in col B, and a value of 1.960 in col C.
Set up lines 117, 118, and 119 to be the same as lines 114, 115 and 116
except use a confidence of 99% in col B and a value of 2.576 in col C.
Format the widths in H111:H119 to 1 decimal place.
In the table below enter the confidence widths from col H.
WIDTH OF
Sample Size
20
Confidence Level
90%
H111=
95%
H114=
99%
H117=
18.
CONFIDENCE
INTERVAL
80
320
H112=
H115=
H118=
H113=
H116
H119=
By comparing widths in the above table, what is the effect of changing sample
size while holding confidence level constant?
Holding confidence level constant, as sample size is increased the width of the
confidence interval _________________________.
19.
20.
When the sample size is quadrupled, what is the ratio of the new width to the old
width? _____________________________
Does this ratio hold regardless of confidence level? ___________
21.
Holding sample size constant, as confidence level is changed from 90% to 95% to
99%, the width of the confidence interval __________________________.
22.
Does this effect hold regardless of sample size? _________________.
23.
Save your file and turn in this sheet with your answers.