Advanced High-School Mathematics

SECTION 6.3 Parameters and Statistics 371 Next, continuing to assume that X anY are independent random variables, we proceed to ...

372 CHAPTER 6 Inferential Statistics In Exercise 6 on page 362 you were asked essentially to investigate the distribution of X ...

SECTION 6.3 Parameters and Statistics 373 (b) Conclude thatf∗f is not differentiable atx= 0. (c) Show that the graph of f∗f is a ...

374 CHAPTER 6 Inferential Statistics x 1 ,x 2 ,...,xnof this random variable. Associated with this sample are Thesample mean: th ...

SECTION 6.3 Parameters and Statistics 375 This shows why it’s best to take “large” samples: the “sampling statistic”X has varian ...

376 CHAPTER 6 Inferential Statistics the sum is divided byn instead of n−1. While the resulting statis- tic is a biased estimate ...

SECTION 6.3 Parameters and Statistics 377 6.3.3 The distribution ofX and the Central Limit Theorem The result of this section is ...

378 CHAPTER 6 Inferential Statistics There are two important observations to make here. First of all, even though we haven’t sam ...

SECTION 6.3 Parameters and Statistics 379 Simulation 4. Let’s take 100 samples of the mean (where each mean is computed from 50 ...

380 CHAPTER 6 Inferential Statistics asn → ∞becomes arbitrarily close to the normal distribution with meanμand variance σ^2 n . ...

SECTION 6.4 Confidence Intervals 381 A very common misconception is that the above two statements mean that the population mean ...

382 CHAPTER 6 Inferential Statistics therefore the random variable Z = Xσ/−√μn is normally distributed with mean 0 and standard ...

SECTION 6.4 Confidence Intervals 383 could be used. To form a 90% confidence interval from a measured meanx, we would replace th ...

384 CHAPTER 6 Inferential Statistics  x−zα/ 2 √σ n ,x+zα/ 2 σ √ n  . Furthermore, we expect that (1−α)×100 percent of the in ...

SECTION 6.4 Confidence Intervals 385 Suppose that you go out and collect 50 samples of the random variable 4×rand and compute t ...

386 CHAPTER 6 Inferential Statistics its unbiased estimate s^2 x, the sample variance. We recall from page 375 thats^2 xis defin ...

SECTION 6.4 Confidence Intervals 387 The philosophy behind the confidence intervals whereσis unknown is pretty much the same as ...

388 CHAPTER 6 Inferential Statistics Exercise As we have already seen it’s possible to use your TI calculators to generate exam ...

SECTION 6.4 Confidence Intervals 389 PROGRAM: CONFINT1 :0→C :Input ”POP MEAN ”, M :Input ”POP STD ”, S :Input ”NO OF EXPER ”, N ...

390 CHAPTER 6 Inferential Statistics that a Gallop Poll survey of 10,000 voters led to the prediction that 51% of the American v ...