Confidence Interval Quiz:
Question One: Below are SAT scores  25^{th} percentile math and verbal and 75^{th} 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.
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/confidenceintervalsforbigtensat.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/theimpactofoutlieronbigtensat.html
Go here for answer to question three:
http://www.dailymathproblem.com/2018/01/evaluationofconfidenceintervalsfrom.html
Estimates of Beta for Growth and Value Stocks
Go here for answer to question two:
http://www.dailymathproblem.com/2016/05/theimpactofoutlieronbigtensat.html
Question Three: Below are the confidence intervals for number of diabetics and nondiabetics in the 50andover population for 2005 and 2015.
What would have been the estimated number of 50andover 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 NonDiabetics 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 50andover population.
Go here for answer to question three:
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

Bristolmyers Squibb Company

1.110

Gilead Sciences

1.45

30

Thermo Fisher Scientific

1.340

Qualcomm

1.57

31

Cocacola Company (the

0.530

Cocacola 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/confidenceintervalandother.html
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