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section8solutions - Stat 104, Section 6 Handout Benny,...

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Unformatted text preview: Stat 104, Section 6 Handout Benny, Thursday, 4pm, SC309 Key Concepts • Project / Regression Report Details • χ 2-test for Goodness-of-Fit/ Independence in two way tables (contingency tables) • Inference for Simple Regression - R 2- s (std. dev, of residuals)- t-test for a regression slope β (and related conf. interval) • Confidence and Prediction intervals at a particular x* • t-test for correlation (equivalent to t-test for slope) Practice Problems 1. Are the digits π of completely random? More specifically, do they come from a uniform distribution. Here are the first 200 digits after the decimal: π = 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 a) What test will we perform? What are the hypotheses for this test? We will perform the chi squared test. The null hypothesis is The alternative hypothesis: At least one probability is not .1. b) Under the null hypothesis above, what is the expected number of each digit? We first calculate the expected number of observations, which is: c) What is the test statistic and its p-value? What is your conclusion? Now, we can calculate the Chi squared statistic: 9 23 8 25 7 12 6 16 5 20 4 22 3 19 2 24 1 20 0 19 pi Freq....
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This note was uploaded on 03/27/2012 for the course STATS 104 taught by Professor Michaelparzen during the Fall '11 term at Harvard.

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section8solutions - Stat 104, Section 6 Handout Benny,...

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