**W2: Assignment 3 Problems**

Problem 1

**Chapter 6** (Probability): Exercises 6.81

**6.81 **Your favorite team is in the final playoffs. You have assigned a probability of 60% that it will win the championship. Past records indicate that when teams win the championship, they win the first game of the series 70% of the time. When they lose the series, they win the first game 25% of the time. The first game is over; your team has lost. What is the probability that it will win the series?

Problem 2

**Chapter 10** (Introduction to Estimation): Exercises 10.11

**10.11 **A random sample of 25 was drawn from a normal distribution with a standard deviation of 5. The sample mean is 80. Determine the 95% confidence interval estimate of the population mean

- b. Repeat part (a) with a sample size of 100.
- c. Repeat part (a) with a sample size of 400.
- d. Describe what happens to the confidence interval estimate when the sample size increases.

.Problem 3

**Chapter 11** (Introduction to Hypothesis is testing): Exercises 11.52

**11.52 A** statistics practitioner wants to test the following hypotheses with *σ* = 20 and *n* = 100: *H*_{0}: *μ* = 100 *H*_{1}: *μ* > 100

- a. Using a = .10 find the probability of a Type II error when
*μ*= 102. - B .Repeat part (a) with a = .02.
- c. Describe the effect on
*β*of decreasing a

Chapter 12 (Inference about a population): Exercises 12.74

**12.74 **Spam is of concern to anyone with an e-mail address. Several companies offer protection by eliminating Spam e-mails as soon as they hit an inbox. To examine one such product, a manager randomly sampled his daily e-mails for 50 days after installing spam software. A total of 374 e-mails was received, of which 3 were spam. Use the Wilson estimator to estimate with 90% confidence the proportion of spam e-mails that get through

**Category:**Economics, General Economics

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