# 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.

- How many experimental outcomes are there?
- 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.