STAT 207. ASSIGNMENT NO. 4

Due on Tuesday, Sept 29, 1998

(The grade for this assignment will be ``handed in'' or ``not handed in'' to indicate if a student has attempted to complete the exercises on their own. The solutions to this assignment will be posted/discussed by Monday, 9/28. I strongly encourage you try to complete exercises on your own before reading the solutions.)

Read Chapter 6.

Review Exercises 5.15, 5.16, 5.17, which we completed in Lecture 8.

Do the following problems:

5.8

5.13

6.2. [Hint: you can list all simple events by finding all possible outcomes since a simple event contains one and only one outcome. A sample space consists of all possible outcomes.]

6.4. [Hint: a) complete the sentence such as ``observing ... in ... week.'' b) use the hint for 6.2. c) follow the Lykins Sporting Goods example given in Lecture 9.]

Exercise A1: Suppose that a study reported that of 250 convicted arsonists, less than 25% were hired as professionals. Ignoring sampling variability, is it safe to conclude that the bulk of arsonists are amateurs rather than professional? Explain.

Exercise A2: Describe the 3 key elements in probability, 3 counting rules and 3 ways of assigning probabilities.

Exercise A3: How many ways can three items be selected from a group of six items? Use the letters A, B, C, D, E and F to identify the items and list each of the different combinations of three items.

Exercise A4: How many permutations of three items can he selected from a group of six? Use the letters A, B, C, D, E, and F to identify the items and list each of the permutations when the three items (B, D, F) are selected.

Exercise A5: Consider the experiment of administering a true-false exam consisting of 10 questions. Each different sequence of answers is an experimental outcome.

  1. How many experimental outcomes are there?
  2. If a student guesses on every question. what is the probability of any particular experimental outcome?

Exercise A6: A company that manufactures toothpaste has five different package designs they want to study. Assuming that one design is just as likely to be preferred by a consumer as any other design, what probability would you assign to a randomly selected consumer preferring each of the package designs? In an actual experiment 100 consumers were asked to pick the design they preferred. The following data were obtained.

 
              Design      1    2    3     4        5
 	      
              Total       5   15   30    40       10
Do the data appear to confirm the belief that one design is just as likely to be selected as another? Explain.