Confidence Intervals

Confidence Interval Quiz:

Question One:   Below are SAT scores -- 25th percentile math and verbal and 75th percentile math and verbal -- for the 14 Big Ten schools.   Calculate the mean and standard deviation of the four SAT scores for the 14 Big Ten Schools.   Use these values to construct the upper bound and the lower bound of 90% confidence intervals for the four mean SAT scores?

What SAT scores have the smallest/largest confidence intervals for Big Ten schools?

Use the confidence intervals to flag Big 10 schools that differ from average Big 10 SAT performance.


The data:  


SAT Scores for Big Ten Schools
Big Ten School
Verbal SAT 25
Math SAT 25
Verbal SAT 75
Math SAT 75
Ohio State
540
610
660
720
University of Michigan
620
660
720
760
Michigan State
420
550
580
690
University of Minnesota
550
620
690
740
University of Iowa
540
620
620
680
Purdue
520
560
630
690
Indiana University
520
540
630
660
Rutgers
520
570
640
690
University of Maryland
580
620
690
730
Northwestern
690
700
760
790
University of Illinois
560
700
670
780
Penn State
530
560
630
670
University of Wisconsin
530
630
650
750
University of Nebraska
490
520
660
670


Go here for answer to question one.
http://www.dailymathproblem.com/2016/05/confidence-intervals-for-big-ten-sat.html


Question Two:  Thirteen of 14 Big Ten Schools are large state universities.   One school – Northwestern is an elite expensive private school. 

Calculate the mean, standard deviation, and 90% confidence interval for the 13 state schools in the Big Ten.

Discuss how and why the confidence interval for the 13 state schools differs from the confidence interval for the mean SAT scores for all 14 Big Ten schools.  

Why might the confidence interval without Northwestern be a better indicator of Big Ten SAT performance than the confidence interval based on all schools in the league?

How does Northwestern SAT scores compare to the upper bounds of the Big Ten SAT confidence interval?

Go here for answer to question two:
http://www.dailymathproblem.com/2016/05/the-impact-of-outlier-on-big-ten-sat.html

Question Three:   Below are the confidence intervals for number of diabetics and non-diabetics in the 50-and-over population for 2005 and 2015.

What would have been the estimated number of 50-and-over diabetics in 2015 if the only factor that had changed was the size of the population?

Can we reject the hypothesis that the only factor impacting the number of diabetics in this age group is population change?



Diabetics and Non-Diabetics 2005 & 2015 (000 Omitted)
2005 Medical Expenditures Panel Survey
Total
Std. Error
LB of 95% CI
UB of 95% CI
Not Diabetic
76,900
2,015
72,900
80,900
Diabetes
12,900
465
11,900
13,800
2015 Medical Expenditures Panel Survey
Total
Std Error
LB of 95% CI
UB of 95% CI
Not Diabetic
93,600
2,672
88,300
98,900
Diabetes
20,300
683
18,900
21,600
Source 2005 and 2015 Medical Expenditure Panel Survey.   Figures in thousands of people for the 50-and-over population.   

Go here for answer to question three:
http://www.dailymathproblem.com/2018/01/evaluation-of-confidence-intervals-from.html


Question Four:   The table below has the estimated stock beta for 35 growth stocks and 35 value stocks.   Use Excel to calculate a 95 percent confidence interval for the mean growth stock beta and the mean value stock beta.

Use Excel finance to observe the skew and kurtosis of the mean growth and value stock betas.

Discuss the results presented here.   Is it possible to create a smaller confidence interval 

Estimates of Beta for Growth and Value Stocks
1
Apple
1.140
Microsoft
1.25
2
AMAZON.COM
1.720
Berkshire Hathaway
0.88
3
Facebook Inc - Class A
0.890
JP Morgan Chase & Co.
1.2
4
Alphabet Inc - Class C Capital Stock
1.300
Exxon Mobil
0.8
5
Visa
1.020
Johnson & Johnson
0.6
6
Home Depot Inc (the
1.070
Bank OF America
1.67
7
Boeing Company (the
1.730
Intel
0.86
8
Mastercard
1.020
Wells Fargo & Company
1.27
9
Abbvie
1.670
Unitedhealth Group Incorporated (de
0.76
10
Comcast Corporation - Class A
1.320
Chevron
1.13
11
Netflix
1.390
Pfizer
0.96
12
Walt Disney Company (the
1.220
Cisco Systems
1.12
13
Nvidia
1.460
Verizon Communications
0.68
14
Mcdonalds
0.690
AT&T
0.43
15
Philip Morris International
0.720
Procter & Gamble Company (the
0.43
16
Adobe Systems
0.810
Citigroup
1.53
17
3M Company
1.070
Merck & Company Inc (
1.1
18
Medtronic PLC. Ordinary Shares
0.750
Dowdupont
1.61
19
Union Pacific
0.850
Oracle
1.12
20
Texas Instruments
1.160
Pepsico
0.64
21
Broadcom
0.560
IBM
1.04
22
Booking Holdings
0.940
Walmart
0.42
23
Accenture Plc Class A Ordinary Shares (ireland
1.090
General Electric Company
0.71
24
Schlumberger N.V.
1.020
Amgen
1.69
25
Paypal Holdings
1.320
Honeywell International
1.11
26
Nike
0.640
Abbott Laboratories
1.75
27
SALESFORCE.COM
1.180
United Technologies
1.13
28
Costco Wholesale
1.010
Caterpillar
1.57
29
Bristol-myers Squibb Company
1.110
Gilead Sciences
1.45
30
Thermo Fisher Scientific
1.340
Qualcomm
1.57
31
Coca-cola Company (the
0.530
Coca-cola Company (the
0.56
32
United Parcel Service
0.910
Eli Lilly And Company
0.43
33
Starbucks
0.580
Conocophillips
1.39
34
Lowes Companies
1.380
Nextera Energy
0.17
35
Micron Technology
1.230
Goldman Sachs Group Inc (the
1.35
Source: Yahoo Finance

Go here for answer to question four:
http://www.dailymathproblem.com/2018/08/confidence-interval-and-other.html

No comments:

Post a Comment