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Topic: exam questions
Replies: 3   Last Post: Mar 12, 1997 6:06 AM

 Messages: [ Previous | Next ]
 Bob Hayden Posts: 2,384 Registered: 12/6/04
exam questions
Posted: Mar 9, 1997 6:12 PM

I've been picking on people posting exam questions and thought I
should post some of my own. Since I am NOT preparing people for the
AP text, my questions are not multiple choice. On the other hand,
they DO incorporate computer printouts which few of the posted
questions have done. Also, this test covers transformations.

*******************************************************************

MATH 230.05 SPRING 1997 HAYDEN'S SECTIONS EXAM I

NAME___________________________________

1. This problem concerns the data from your text on the
Whistler Mountain Ski Area. Here is a printout for this
data.

MTB > retr 'stats1a/smt04.10'
WORKSHEET SAVED 1/10/1996

MTB > print c1-c5
ROW Lift length v.rise seats speed

1 Peak Chair 1060 401 3 0
2 Blue Chair 1048 267 2 0
3 Green Chair 1833 424 4 1
4 Black Chair 1752 540 3 0
5 Olympic Chair 729 142 3 0
6 Express Gondola 5012 1157 10 1
7 Quicksilver Quad 2050 647 4 1
8 Alpine T-Bar Two 841 200 2 0
9 Alpine T-Bar One 943 224 2 0
10 Red Line Quad 2495 553 4 1
11 Orange Chair 1238 386 2 0
12 Platter Lift 171 19 1 0
13 Scampland Handle 1 117 22 1 0
14 Scampland Handle 2 150 35 1 0

MTB > describe c2-c5

N MEAN MEDIAN TRMEAN STDEV SEMEAN
length 14 1388 1054 1192 1269 339
v.rise 14 358.4 326.5 320.1 307.6 82.2
seats 14 3.000 2.500 2.583 2.287 0.611
speed 14 0.286 0.000 0.250 0.469 0.125

a. The file contains a column of case labels and four
columns of data.

i. Which column(s) contain(s) categorical data?

ii. Which column(s) contain(s) measurement data?

iii. Which column(s) contain(s) measurement data
that could be treated as categorical data?

b. The data on number of seats can be treated as
grouped data.

i. Find the five-number summary for this data.
____________________

ii. Make a (full) boxplot for this data. Show

iii. What can you say about the mode for this
data?

iv. In the space below, find the mean, variance,
and standard deviation of this data. Show
all work, including residuals. There may be
more spaces than you need.

_____ _____ _____ _____ _____ _____ _____

_____ _____ _____ _____ _____ _____ _____

_____ _____ _____ _____ _____ _____ _____

_____ _____ _____ _____ _____ _____ _____

_____ _____ _____ _____ _____ _____ _____

_____ _____ _____ _____ _____ _____ _____

mean = ______

variance = ________ standard deviation = ________

v. List the names of all the measures of center
you have studied in this course and explain
whether or not it would matter which one you
used for this data and why.

c. The data in C5 are coded as 1 for a high speed lift
and 0 for all other lifts. Circle and label on the
Minitab printout above the proportion of high speed
lifts.

d. Based on the stem and leaf displays below, describe
the distribution of each variable. Put the
descriptions on the Minitab printout below.

Make your own stem-and-leaf for the "length" data.
Be sure to choose an appropriate scale!

MTB > stem c3-c5

Stem-and-leaf of v.rise N = 14
Leaf Unit = 100

4 0 0001
(4) 0 2223
6 0 4455
2 0 6
1 0
1 1 1

Stem-and-leaf of seats N = 14
Leaf Unit = 0.10

3 1 000
7 2 0000
7 3 000
4 4 000
1 5
1 6
1 7
1 8
1 9
1 10 0

Stem-and-leaf of speed N = 14
Leaf Unit = 0.010

(10) 0 0000000000
4 1
4 2
4 3
4 4
4 5
4 6
4 7
4 8
4 9
4 10 0000

e. Suppose you did not like the look of the stem and
leaf for the speed variable so you transformed it
by taking square roots and made a stem and leaf
display of the results. How would it compare to
the original stem and leaf for this variable?

f. Based only on the information printed on this test
(not on the additional Minitab handout), which
variables do you think are good candidates for
transformation? ___________ Explain why in each
case.

You have some additional Minitab printout
concerning some transformations of this data.

g. Which variable was transformed on your printout?
_________

h. Find the following statistics for the original
version of the data before it got transformed.

minimum _________ maximum _________

Q1 _________ range _________

median _________ IQR _________

Q3 _________ 75th percentile _________

All of these are statistics of one type, which are
called _________ statistics.

i. What is the name of the first transformation that
was tried? ____________ Be as complete and precise
as possible.

j. What is the name of the second transformation that
was tried? ____________ Be as complete and precise
as possible.

k. There are a number of displays on your Minitab
transformation printout. Next to each one, write a
description of the distribution. You should
include comparative information as to which looks
the most normal, skewed, or whatever. BE SURE TO
TURN IN THIS PRINTOUT WITH YOUR EXAM!

l. Which of the transformations do you think was most
effective in making the data more normally
distributed? ____________ Explain why you picked
this transformation.

2. For the data below, find the mean, variance, and standard
deviation. Fill in all the spaces in the table.

2
X X -`X (X -`X)

1 _____ _____ mean _____

11 _____ _____

7 _____ _____ variance _____

3 _____ _____

standard deviation _____

------------------------- Minitab Sheet ------------------------------

MTB > let c10=sqrt('seats')
MTB > let c11=logten('seats')
MTB > stem 'seats' c10 c11

Stem-and-leaf of seats N = 14
Leaf Unit = 0.10

3 1 000
7 2 0000
7 3 000
4 4 000
1 5
1 6
1 7
1 8
1 9
1 10 0

Stem-and-leaf of C10 N = 14
Leaf Unit = 0.10

3 1 000
3 1
7 1 4444
7 1 777
4 1
4 2 000
1 2
1 2
1 2
1 2
1 3 1

Stem-and-leaf of C11 N = 14
Leaf Unit = 0.010

3 0 000
3 1
3 2
7 3 0000
7 4 777
4 5
4 6 000
1 7
1 8
1 9
1 10 0

MTB > stop
*** Minitab Release 9.1 *** Minitab Inc. ***
Worksheet size: 100000 cells

--

_
| | Robert W. Hayden
| | Department of Mathematics
/ | Plymouth State College MSC#29
| | Plymouth, New Hampshire 03264 USA
| * | Rural Route 1, Box 10
/ | Ashland, NH 03217-9702
| ) (603) 968-9914 (home)
L_____/ hayden@oz.plymouth.edu
fax (603) 535-2943 (work)

Date Subject Author
3/9/97 Bob Hayden
3/10/97 Paul Velleman
3/10/97 Bob Hayden
3/12/97 Chris Olsen