INFO 1020 Week 5 Class Notes
INFO 1020 Week 5 Class Notes INFO 1020
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This 6 page Class Notes was uploaded by Alexandra Tilton on Saturday February 6, 2016. The Class Notes belongs to INFO 1020 at University of Denver taught by Ray Boersema in Winter 2016. Since its upload, it has received 23 views. For similar materials see Analytics II: Statistics and Analysis in Information System at University of Denver.
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Date Created: 02/06/16
INFO 1020: Analytics II Class Notes Mon. 2/1 Chapter 8: Interval Estimation • Interval Estimate vs. Point Estimate •Point Estimate: single value, from sample, best guess at population parameter. P(correct) = 0 •Interval Estimate: set of values, from sample, expected to contain the population parameter. P(correct) > 0 • Conﬁdence Interval •Range of numbers (low #, high #) •Arange of numbers derived from sample data and probability theory that likely contains the population parameter (not guaranteed) • Conﬁdence Level •The probability that the population parameter is actually in the conﬁdence interval • Level of Signiﬁcance •1-Conﬁdence Level •Denoted with α • Margin of Error •Anumber we calculate and then add to and subtract from a sample statistic to get the Conﬁdence Interval Alexandra Tilton Page ▯1 of ▯6 • Margin of Error for a Conﬁdence Interval for Mean using Standard Deviation • Z: use corresponding z values on sheet • σ: standard deviation of population • n: sample size Conﬁdence Interval is found by: • • ̄ +/- Margin of Error • ̄ +/- z* α/sqrt(n) • Alarger sample size creates a narrower conﬁdence interval • Ahigher z-value gives a wider conﬁdence interval • Example: What is the average INFO 1020 grade? • Sample: Spring Roster • n = 32 • ̄ = 88.4 • σ = 8 • 88.4 +/- 1.960 * 8/sqrt 32 = 85.6, 91.2 • What is the Margin of Error for the Conﬁdence Interval for Mu using S • M.E.: t*s/sqrt n • The t-distribution • Almost normal • Wider/lower than normal • Many of them • Degrees of Freedom • n-1 (in chapter 8) • What formula for Conﬁdence Interval for ▯ when σ is unknown • ̄: sample mean • t: =ABS((T.INV(1/2α,n-1))) Alexandra Tilton Page ▯2 of ▯6 • s: sample stdev • n: sample size • Margin of Error in Determining Conﬁdence for p • Margin of Error = z* (sqrt(pbar(1-pbar)/n) • Formula to determine Conﬁdence Interval for p? • Pbar +/- Margin of Error • Example: • Asample of 200 voters showed that 42% support… • Find the 95% Conﬁdence Interval for p INFO 1020: Analytics II Class Notes Wed. 2/3 Chapter 9: Hypothesis Tests • Developing Null and Alternative Hypothesis Hypothesis: a proposed statement of truth. It stays true until proven • false • Hypothesis Test: a process that provides opportunity to deny the hypothesis • Two hypotheses in statistics** • Null Hypothesis - Ho: μ = 32 • Alternative Hypothesis - Ha: μ ≠ 32 OR μ > 32 OR μ < 32 • H oust contain an equal sign • So that we can build and use a ﬁxed distribution ō x possibilities • H os the hypothesis being challenged because… • it is the current status quo that needs to be challenged Alexandra Tilton Page ▯3 of ▯6 • H as where we land if we reject H o H is where we land if we fail to rejectH • o o • Order of hypotheses • Write H aodH togeaher • One-tail vs two-tail test • Two tailed test: H cantains ≠ • One tailed right test: H cantains > • One tailed left test: H aontains < • Type I and Type II Errors • Type I: Reject a true H o • Type II: Fail to reject a false H o • Relationship between Type I and Type II error • If the P of one goes up, the other one goes down • Can you decrease the probability of both types of errors • You can, with a bigger sample or a better sample • Visual T F Reject Type I Good Fail to Good Type II Reject • Level of Signiﬁcance • 1-Level of Conﬁdence Denoted as: α (alpha) • • The maximum allowable probability of a Type I Error • Standard is 5% • Six steps of every hypothesis test 1. Write the two hypotheses 2. Specify the α value Alexandra Tilton Page ▯4 of ▯6 3. Sample data; Test statistic 4. P-Value 5. Decision Interpretation of the test results 6. • Hypotheses Choices • (In this section) see above ** • What is a test statistic? • Either a formula or the result of evaluating formula • Test statistic for this type of test (this section)? • Z that we calculate • ̄-μ/(σ/sqrt(n)) • What is the P-Value approach to ﬁnishing a hypothesis test? • P-Value: The actual probability of a Type I error if we reject H o • Decision Rules: • Reject H if P-value < α o • Fail to reject Hoif P-value > α • How can Excel give the P-Value • =2*Norm.S.DIST(zcalc,1) • 2 is for the two tails • This is for H a • Omit 2 if you have H < ar > • If you want tail with 3, put in -3 (make sure z calc is negative) • Example Problem • Someone says average person lives 600 miles from home • H o μ = 600 • H a μ ≠ 600 • α = .05 Alexandra Tilton Page ▯5 of ▯6 • n = 20 • ̄ = 800 • σ = 100 z calc = (800-600)/(100/sqrt 20) = 8.6 • • P-Value: =2*Norm.S.DIST(-8.6,1) = 7.97 E -18 • P-Value is less than σ, REJECT H o • Sample evidence indicates that μ is probably wrong Alexandra Tilton Page ▯6 of ▯6
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