I. Find the sales data for Apple here: http://images.apple.com/pr/pdf/q1fy13datasum.pdf. (30 points)
a. How would you estimate the average revenues for Q1'13 using operating segments? Which is the best method? How would you interpret an average across countries here?
b. Is there enough information to estimate the average using the method you recommend?
c. In product summary why it is important to have the units listed? If you want to estimate average revenue for Apple products do you need to use the units? How?
II. Review the data in Table 1. It covers the median income for the top 25 Georgia counties. (50 points)
a. If John earns $62,591 annually in Henry County what would change for him if he moves to Cherokee county?
b. You want to demonstrate this data, how would you categorize it?
c. If you want to show the number of counties with a median income within a certain range how do you identify those ranges? How many bins you will choose? What kind of representation you will choose?
d. Use Excel to draw the graph and submit it as part of your work.
e. Consider the Median Income as a variable, report Mean, Median, STD, Variance and Quartiles for it.
f. Would you identify the counties which are between 25 percentile and 75 percentile (second and third quartiles)?
|
Table 1
|
|
Rank
|
County
|
Median
|
|
1
|
Forsyth
|
$84,567
|
|
2
|
Fayette
|
$77,491
|
|
3
|
Oconee
|
$74,630
|
|
4
|
Columbia
|
$68,986
|
|
5
|
Cherokee
|
$66,972
|
|
6
|
Henry
|
$63,892
|
|
7
|
Paulding
|
$63,663
|
|
8
|
Harris
|
$63,351
|
|
9
|
Cobb
|
$62,893
|
|
10
|
Coweta
|
$59,848
|
|
11
|
Gwinnett
|
$58,732
|
|
12
|
Bryan
|
$58,092
|
|
13
|
Lee
|
$57,044
|
|
14
|
Fulton
|
$56,313
|
|
15
|
Pike
|
$55,674
|
|
16
|
Effingham
|
$54,678
|
|
17
|
Monroe
|
$53,805
|
|
18
|
Dawson
|
$53,215
|
|
19
|
Rockdale
|
$51,265
|
|
20
|
Douglas
|
$50,798
|
|
21
|
Pickens
|
$50,798
|
|
22
|
Houston
|
$50,733
|
|
23
|
Jackson
|
$50,591
|
|
24
|
Walton
|
$50,321
|
|
25
|
Newton
|
$50,137
|
|
26
|
DeKalb
|
$50,092
|
III. Display the data in Table 1 using Stem Leaf approach and dot plot. (20 points)
IV. If X has a Normal distribution of N(10, 25) Please find
a) P ( X > 35)
b) P ( -15 < X < 35)
c) P ( X < 25)
d) If X is the average spending on a new notebook and I would like to find the top 5 percent big spenders how should I approach this?
V. I have chosen a sample of 50 students from 5000 students to study the GPA distribution across campus.
a. Can I assume the sample average has a Normal distribution?
b. If I am estimating standard deviation should I use a correction factory?
c. If in this sample GPA average is 2.25 and if the standard deviation of population GPA is 1.5 and population mean is 2.5 then what is the Normal distribution for population mean?
d. Please identify the area which includes population mean with 90 percent possibility.
|
Confidence Level
|
α
|
α/2
|
Area
|
zα/2
|
|
90%
|
.10
|
.05
|
.95
|
1.645
|
|
95%
|
.05
|
.025
|
.975
|
1.960
|
|
99%
|
.01
|
.005
|
.995
|
2.576
|
VI. In a sample of 101 Atlanta residents average income is $56,560. If the standard deviation of income in Atlanta area is $12,000 then please do the following:
a. 90% confidence interval for population mean
b. 95% confidence interval for population mean
c. 99% confidence interval for population mean
d. If a statistician report Atlanta median income is $55,733 since you can assume population mean is Normally distributed can you accept this number based on this number? Is there a confidence interval where $55,733 is smaller than lower bound or
higher than higher bound?
| Degree of Freedom |
Area in Upper Tail |
| .20 |
.100 |
.050 |
.025 |
.010 |
.005 |
| 15 |
.866 |
1.341 |
1.753 |
2.131 |
2.602 |
2.947 |
| 16 |
.865 |
1.337 |
1.746 |
2.120 |
2.583 |
2.291 |
| 17 |
.863 |
1.333 |
1.740 |
2.110 |
2.567 |
2.898 |
| 18 |
.862 |
1.330 |
1.734 |
2.101 |
2.520 |
2.878 |
| 19 |
.861 |
1.328 |
1.729 |
2.093 |
2.539 |
2.861 |
VII. In a sample of 20 Atlanta residents average income is $57,960. If the standard deviation of income in Atlanta area is not known but based on your sample it is $10,000 then please do the following:
a. What is your degree of freedom?
b. 90% confidence interval for population mean
c. 95% confidence interval for population mean
d. 99% confidence interval for population mean
e. If a statistician report Atlanta median income is $55,733 since you can assume population mean is Normally distributed can you accept this number based on this number? Is there a confidence interval where $55,733 is smaller than lower bound or higher than higher bound?