Week 5: Homework Assignment 2
Homework Assignment 2: 25 PTS
Instructions:
1. You need to show ALL your calculations to merit full points. You’ll get partial points
if you show the final answers only.
2. Round off all calculations to four decimal places (e.g., 9.3245). If the answer is in
percentage, round your final answer to 2 decimal places (e.g., 8.64%)
Problem #1. Bingo’s bookstore wants to determine how much of its floor space to use
for books, and how much for games and movies. 500 customers are asked if they visit
the store primarily for books, or primarily for games and movies. The customers are also
divided by age group. The results of this survey are shown in the contingency table below:
Books Games & Movies Total
Under 20 years old 90 160 250
20 years old or more 300 50 350
Total 390 210 600
One customer is selected at random. Find the following probabilities. Express your
answers as percentage. (9 points)
a. The person is 20 years old or more and primarily visits the store for games and
movies. (2 pt)
b. The person is 20 years old or more or primarily visits the store for books. (2 pt)
c. The person is under 20 years old given that he/she visits the store for games and
movies. (2 pt)
d. Are age & primary merchandise statistically independent events? (3 pts)
Tip: Perform test of independence. Do not use Chi-Square – this is not part of
this week’s coverage.
Problem#2. A small rental franchise keeps detailed records of vehicles being returned
damaged. In one year, 540 out of 3000 automobiles and 280 out of 2000 trucks were
returned damaged. A total of 4180 vehicles were not returned damaged.
Are type of vehicle and damaged/undamaged statistically independent events? (3
points)
Tip: Perform the test of independence. Constructing a contingency table may also help.
Do not use Chi-Square – this is not part of this week’s coverage.
Problem #3. For each of the following, state whether the events created are mutually
exclusive and whether they are collectively exhaustive. So, for each item below, you are
expected to provide two answers: (1) whether mutually exclusive or not, and (2) whether
collectively exhaustive or not. (4 points)
a. Undergraduate business students were asked whether they were sophomores or
juniors.
b. Each respondent was classified by the type of car he or she drives: sedan, SUV,
American, European, or Asian.
c. People were asked, “Do you currently live in (i) an apartment or (ii) a house?”
d. A product was classified as defective or not defective.
Problem #4. Do males or females feel more tense or stressed out at work? A survey of
employed adults conducted online by Harris Interactive on behalf of the American
Psychological Association revealed the following (4 points)
FELT TENSE OR STRESSED OUT AT WORK
GENDER YES NO
MALE 244 495
FEMALE 282 480
Based on the contingency table above:
a. Give an example of a simple event
b. Give an example of a joint event.
c. What is the complement of “Felt Tense or Stressed Out at Work”?
d. Why is “Male and Felt Tense or Stressed Out at Work” a joint event?
Problem #4. Do Americans prefer a name-brand milk or store brand milk? A survey was
conducted by Harris Poll Interactive, Inc. in November 2014. Suppose the results, based
on 1,138 females and 1,138 males, were as follows: (5 points)
GENDER
PREFERENCE MALE FEMALE TOTAL
NAME-BRAND MILK 319 341 660
STORE-BRAND MILK 717 649 1,366
SOMETHING ELSE 102 148 250
TOTAL 1,138 1,138 2,276
a. Given that an American is a male, what is the probability that he prefers namebrand milk? (2 pts)
b. Is preference independent of gender? Tip: Perform the test of independence. (3
pts)
Tutorial for Homework Assignment 2
