# CHRIS HARROW HAWKEN SCHOOL @CHRIS_HARROW Nspired CAS and Statistics.

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CHRIS HARROW HAWKEN SCHOOL HTTP://CASMUSINGS.WORDPRESS.COM/ CASMUSINGS@GMAIL.COM CDHARR@HAWKEN.EDU @CHRIS_HARROW Nspired CAS and Statistics

PHILOSOPHY Philosophical Goals for my class  Eliminate Tables  Minimize Tools  Maximize Depth, Understanding, & Flexibility CAS Technology  Think in terms of functions  Algebraic manipulations aren’t central.  Keep focus on the problem not the computations. USACAS 9: http://bit.ly/USACAS-9http://bit.ly/USACAS-9  July 18-19, 2015 in Cleveland, OH  Focus on CAS before calculus, but including statistics

Nspired CAS and Statistics WHAT IS A LINEAR REGRESSION? Click here to Download LinReg File Least Squares Line Many people perform linear regressions on data without ever considering what is happening. I initially wrote this for an Honors Algebra 2 course to explain this line WITHOUT Calculus http://bit.ly/LinReg_Derivation

Nspired CAS and Statistics ENHANCING BINOMIAL PROBABILITIES Binomial Probabilities:  Combinatorics can be complicated:  nCr() Command can give single values or lists

Nspired CAS and Statistics ENHANCING BINOMIAL PROBABILITIES Binomial Probabilities:  Binomial formula important for derivation and understanding, but not for practical use.  CAS expand() command  What do a, b, and n represent?  Better yet, the Nspire allows open variable names (no spaces)

Nspired CAS and Statistics ENHANCING BINOMIAL PROBABILITIES Two fair eight-sided dice (the faces are labeled 1-8) are tossed at once. What is the probability that at least one of them shows “7”?

Nspired CAS and Statistics ENHANCING BINOMIAL PROBABILITIES CAS Insight #2: Change the coefficients!  VISUAL understanding, not just polynomial  See the entire sample space/pdf at once

Nspired CAS and Statistics ENHANCING BINOMIAL PROBABILITIES With Nspire power, you can approach this several ways with summations.

Nspired CAS and Statistics NORMAL PROBABILITY DISTRIBUTIONS DECREASING EMPHASIS ON z-SCORES Computing normal distribution areas To use a table of values for normal scores, you need to convert non-standard information into z-scores. The Nspire makes that irrelevant:  Normcdf(lower, upper [, mean, st.dev]) z-scores are important, they just aren’t THAT critical  We no longer use root or trig tables

Nspired CAS and Statistics NORMAL PROBABILITY DISTRIBUTIONS Computing normal distribution area Under given testing conditions, a golf ball legal for tournament play may not travel more than 300 yards. Manufacturers want balls that will travel as close to the 300 yards without exceeding that distance. One manufacturer determined the distances traveled for its golf balls are normally distributed with a mean of 295 yards and a standard deviation of 3 yards. What is the probability a random ball will travel too far?

Nspired CAS and Statistics NORMAL PROBABILITY DISTRIBUTIONS Computing normal distribution area

Nspired CAS and Statistics NORMAL PROBABILITY DISTRIBUTIONS Now assume the manufacturing process can control the mean distance traveled. What mean should it use so that no more than 1% of the golf balls travel more than 300 yards?  There’s a time for invNorm()

Nspired CAS and Statistics NORMAL PROBABILITY DISTRIBUTIONS Computing normal distribution area This is area under a curve. Differentiate instruction. For calculus students in class, mention integrals to reinforce.

Nspired CAS and Statistics WHAT IS A CONFIDENCE INTERVAL? HOW CAN YOU COMPUTE ONE? The mean lead level of 35 crows in a random sample from a region was 4.90 ppm and the standard deviation was 1.12 ppm. Construct a 95 percent confidence interval for the mean lead level of crows in the region.  You can get this through a black-box confidence z-interval command

Nspired CAS and Statistics WHAT IS A CONFIDENCE INTERVAL? HOW CAN YOU COMPUTE ONE? Emphasize understanding  Continue to use normCdf()  invNorm() variation

Nspired CAS and Statistics WHAT IS A CONFIDENCE INTERVAL? HOW CAN YOU COMPUTE ONE? Emphasize understanding  Clever variation from a student due to CAS/Nspire familiarity with lists  Equivalent approach using normCdf doesn’t work:  Be flexible, adapt.

Nspired CAS and Statistics MULTIPLE APPROACHES TO FINDING MINIMAL SAMPLE SIZES You run the safety division of a car manufacturer and have a budget large enough to run 120 stopping distance tests on a new vehicle for which it has been determined that  =12 feet. Can you estimate the mean stopping distance to within 2 feet of the true mean stopping distance with 95% confidence?  Distance approach (z-scores do matter)  Distance=(num. of s.d.s)(size of s.d.)=

Nspired CAS and Statistics MULTIPLE APPROACHES TO FINDING MINIMAL SAMPLE SIZES  The mean is irrelevant. Re-centering a normal distribution doesn’t change its shape.  Assume different means and use your CAS:

Nspired CAS and Statistics Attend USACAS-9  July 18-19, 2015  Cleveland, OH  Hosted by MEECAS & Hawken School  Sponsored by TI and others  http://bit.ly/USACAS-9 http://bit.ly/USACAS-9  See you there!!