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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.
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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 c1c5 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 TBar Two 841 200 2 0 9 Alpine TBar 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 c2c5
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 fivenumber summary for this data. ____________________
ii. Make a (full) boxplot for this data. Show your work.
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 stemandleaf for the "length" data. Be sure to choose an appropriate scale!
MTB > stem c3c5
Stemandleaf 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
Stemandleaf 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
Stemandleaf 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 Stemandleaf 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 Stemandleaf 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 Stemandleaf 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 032179702  ) (603) 9689914 (home) L_____/ hayden@oz.plymouth.edu fax (603) 5352943 (work)



