Advanced High-School Mathematics

SECTION 6.4 Confidence Intervals 391 Ifb 1 , b 2 ,...,bnare the observed outcomes, i.e., bi =    1 if type A is observed; 0 ...

392 CHAPTER 6 Inferential Statistics The reason is the highly skewed nature of a binomial population with parameterpvery close t ...

SECTION 6.4 Confidence Intervals 393 margin of error also decreases the confidence level. A natural question to ask is whether w ...

394 CHAPTER 6 Inferential Statistics We can similarly determine sample sizes needed to a given bound on the margin of error in t ...

SECTION 6.5 Hypothesis Testing 395 to test the accuracy of this claim. This claim can be regarded as a hypothesis and it is up t ...

396 CHAPTER 6 Inferential Statistics Again, in the U.S. judicial justice system, it is assumed (or at least hoped ) thatαis very ...

SECTION 6.5 Hypothesis Testing 397 Continuing the above example, assume more realistically that we didn’t know in advance the va ...

398 CHAPTER 6 Inferential Statistics (E) Type I error: get drenched Type II error: carry an umbrella, and it rains Mr. Surowski ...

SECTION 6.5 Hypothesis Testing 399 6.5.1 Hypothesis testing of the mean; known variance Throughout this and the next section, th ...

400 CHAPTER 6 Inferential Statistics (Remember, the smaller this error becomes, the larger the probability βbecomes of making a ...

SECTION 6.5 Hypothesis Testing 401 6.5.2 Hypothesis testing of the mean; unknown variance In this setting, the formulation of th ...

402 CHAPTER 6 Inferential Statistics H 0 : p=. 55 , Ha:p <. 55. The test statistic would then be Z = P̂−p √̂ P(1−P̂)/n , whic ...

SECTION 6.5 Hypothesis Testing 403 represents taking two independent samples; we won’t go into the appro- priate statistic for e ...

404 CHAPTER 6 Inferential Statistics Suppose that a coin is tossed 320 times, with the total number of “heads” being 140. At th ...

SECTION 6.6 χ^2 and Goodness of Fit 405 Active Ingredient (in milligrams) Pharmacy 1 2 3 4 5 6 7 8 9 10 Name brand 245 244 240 2 ...

406 CHAPTER 6 Inferential Statistics given by χ^2 = ∑(ni−E(ni))^2 E(ni) , where the sum is over each of thekpossible outcomes (i ...

SECTION 6.6 χ^2 and Goodness of Fit 407 Z = N 1 −np » np(1−p) is approximately normally distributed with mean 0 and standard dev ...

408 CHAPTER 6 Inferential Statistics (The above calculation can be done on your TI-83, using 1−χ^2 cdf(0, 4 ,1). The third argum ...

SECTION 6.6 χ^2 and Goodness of Fit 409 In general, experiments of the above type are calledmultinomial experiments, which gener ...

410 CHAPTER 6 Inferential Statistics PROGRAM: CHISQ : Input“ DF ”,N : 0→S :For(I, 1 ,N+ 1) :S+ (L 1 (I)−L 2 (I))^2 /(L 2 (I))→S ...