BrownMath.com → Statistics → Spr15 ME50 → Probability Lab
Updated 25 Mar 2015

# Probability Lab (Due on 24 Mar)

portions Copyright © 2014–2015 by Stan Brown

## Data Collection

Use the data sheet at the end of this lab, or separate paper laid out the same way. Pick any 29 TC3 students, some men and some women, some who live on campus and some who don’t. Ask the questions, and fill in the values of the following categorical variables for each student:

• Gender?
• Live on or off campus?
• Take any evening class? (An evening class is one that starts at 4:30 or later.)
• Eye color? (Pick one of these six only: black, blue, brown, gray, green, hazel.)
• Favorite movie genre? (Pick one out of these six only: Action/Adventure, Comedy, Drama, Horror/Thriller, Romance, Other.)

Add yourself as the 30th person.

## Directions for This Lab

• On separate paper, show your work and then your answer for the first question, your work and then your answer for the second question, and so on. You must show your work including tallies for full credit. I recommend you use your calculator for calculations, but you may use Excel instead if you wish.
• Check the numbers you enter in your calculator! It’s pretty bad if your answers don’t match your data.
• Do a professional job: Write neatly and legibly, remove any “decorative fringe” from the paper, and so forth. I recommend pencil and eraser because correcting mistakes in ink is a bear. Word processing is also acceptable.
• Hand in your data sheet. I can’t accept the lab without the full set of raw data.
• Don’t hand in the questions.
• Staple all pages neatly before you come to class, because loose sheets and insecure fasteners cost a 10% penalty. You don’t need a report cover.

## Two-Way Tables

Question 1 (9 points):  Make three two-way tables to summarize the data:

• On/Off Campus versus Evening Class.
• Gender versus favorite Movie Genre.
• Eye Color versus Gender.
OnCampus OffCampus |||| || |||| | |||| |||| |||| ||
OnCampus OffCampus Total 7 6 13 5 12 17 12 18 30

For each two-way table, go once through your raw data and put a tally mark in the appropriate box for each student, like the table at left above. Then count the tallies to make a final table like the one at right. Fill in row and column totals, and verify that the totals add each way to your sample size of 30.

For some tables, you will need more than two rows or columns.

## Data Analysis

Question 2 (18 points):  Assume that your data are representative of TC3 students in general. Find each probability below, and interpret it in an English sentence.

Example: P(Evening).
Answer: P(Evening) = 13/30 or about 43%. There’s a 43% chance that any randomly selected student takes evening classes. [Equally acceptable: 43% of students take evening classes.]

Use your own data for the rest of these, and remember to show your computations.

(a) P(male)
(b) P(lives on campus)
(c) P(comedyC) — I didn’t mean P(comedy).
(d) P(female and blue eyes)
(e) P(evening class or lives on campus)
(f) P(male or prefers horror/thriller)
(g) P(evening class | lives off campus)
(h) P(female and prefers comedies)
(i) P(brown eyes | male)

Question 3 (3 points):  According to your sample, not what you may know or think about students in general, is prefers romance movies mutually exclusive with male? Explain.

Question 4 (3 extra-credit points):  According to your sample, not what you may know or think about students in general, are lives on campus and takes evening classes independent events? Explain.

## Acknowledgement

This lab was adapted from an assignment created by Benjamin Kirk for his classes, and is used with his kind permission.

StudentGenderOn/Off CampusEvening ClassEye ColorMovie Genre
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You

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