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### 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 1.14 Microsoft 1.25 2 AMAZON.COM 1.72 Berkshire Hathaway 0.88 3 Facebook Inc - Class A 0.89 JP Morgan Chase & Co. 1.2 4 Alphabet Inc - Class C Capital Stock 1.3 Exxon Mobil 0.8 5 Visa 1.02 Johnson & Johnson 0.6 6 Home Depot Inc (the 1.07 Bank OF America 1.67 7 Boeing Company (the 1.73 Intel 0.86 8 Mastercard 1.02 Wells Fargo & Company 1.27 9 Abbvie 1.67 Unitedhealth Group Incorporated (de 0.76 10 Comcast Corporation - Class A 1.32 Chevron 1.13 11 Netflix 1.39 Pfizer 0.96 12 Walt Disney Company (the 1.22 Cisco Systems 1.12 13 Nvidia 1.46 Verizon Communications 0.68 14 Mcdonalds 0.69 AT&T 0.43 15 Philip Morris International 0.72 Procter & Gamble Company (the 0.43 16 Adobe Systems 0.81 Citigroup 1.53 17 3M Company 1.07 Merck & Company Inc ( 1.1 18 Medtronic PLC. Ordinary Shares 0.75 Dowdupont 1.61 19 Union Pacific 0.85 Oracle 1.12 20 Texas Instruments 1.16 Pepsico 0.64 21 Broadcom 0.56 IBM 1.04 22 Booking Holdings 0.94 Walmart 0.42 23 Accenture Plc Class A Ordinary Shares (ireland 1.09 General Electric Company 0.71 24 Schlumberger N.V. 1.02 Amgen 1.69 25 Paypal Holdings 1.32 Honeywell International 1.11 26 Nike 0.64 Abbott Laboratories 1.75 27 SALESFORCE.COM 1.18 United Technologies 1.13 28 Costco Wholesale 1.01 Caterpillar 1.57 29 Bristol-myers Squibb Company 1.11 Gilead Sciences 1.45 30 Thermo Fisher Scientific 1.34 Qualcomm 1.57 31 Coca-cola Company (the 0.53 Coca-cola Company (the 0.56 32 United Parcel Service 0.91 Eli Lilly And Company 0.43 33 Starbucks 0.58 Conocophillips 1.39 34 Lowes Companies 1.38 Nextera Energy 0.17 35 Micron Technology 1.23 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