business stat homwork question

lU,17 Overloading in the trucking industry. Alt.hough illegal,
overloading is common in the trucking industry; A state
LOADS highway planning agency (Minnesota Department of
Transportation) monitored the movements of overYr””eight
trucks on an interstate highway using an unmanned, oomputerized scale that is built into the highway. Unkno·w’n
to the truckers, the scale weighed their vehicles a tbe ~
passed over it. Each day’s proportion of 1 week’s total
truck traffic (five-axle tractor truck semitraile rs) is
shown in the first column of the table below. During the
same week, the number of overweight trucks per day is
given in the second column. This information is saved
in the accompanying file. The planning agency would
like to know whether the number of overweight trucks
per week is distributed over the 7 days of the week
in direct proportion to the volume of truck traffic. Test
using a = .05. x2 = 12.374
Day
Proportion
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
.191
.198
.187
.180
.155
.043
.046
Number
90
82
72
70
51
18
31
10.18 Political representation of religious groups. Do those
elected to the U.S. House of Representatives really “repusHoR resent” their constituents demographically? This was a
question of interest in Chance (Summer 2002). One of
several demographics studied was religious affiliation. The
accompanying table gives the proportion of the U.S. population for several religions, as well as the number of the 435
seats in the House of Representatives that are affi liated
with that religion. Give your opinion on whethe1:-;or not the .
House of Representatives is statistically representative of
the religious affiliations of their constituents in the United
States. i 2 ,- 17 4. 17
Religion
Proportion of U.S.
P0ioalation
Number of Seats
in House
Jewish
Other
.02
.66
30
227
Totals
1.00
435
– – – – – – – – – – – – – — · ·—–· ——- -·
117
.28
Catholic
61
.04
Methodist
10.27 Are travel professionals equitably paid? Business Travel
News (July 17, 2006) reported the results of its annual
TRVPRo Travel Manager Salary & Attitude survey. A total of 277
travel professionals, 103 males and 174 females, partjci-
pated in the 2005 survey. One question asked for the travel
professional’s opinion on the fairness of his/her salary.
Responses were classified as “salary too low,” “equitable/
fair,” or “paid well.” The table below gives a breakdown of
the responses in each category by gender.
Males
Salary too low
Equitable/fair
Paid well
29
58
16
Totals
103
a. Find the proportion of male travel professionals who
believe their salary is too low and compare it to the proportion of female travel professionals who believe their
salary is too low.. 282 : .511
b. Repeat part a but compare the proportions who believe
their salary is equitable/fair. .563 : .368
c. Repeat part a but compare the proportions who believe
they are paid well . .155; .121
d. Based on the comparisons, parts a-c, do you think
opinion on the fairness of a travel professional’s salary
differs for males and females? Yes
e. Refer to part d. Conduct the appropriate statistical test
using a= .10. 1= =·, 1 … ,:: ·
f. Construct and interpret a 90% confidence interval for
the difference between the proportions of part a.
–
_ _
..J
~
– – – – L-A –
n _ ,c ___
,._ _
;,1 _
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1
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}0.33 Creating menus to influence others. Refer to the Journal
t
of Consumer Research (Mar. 2003) study on influencing
;.MENU3 the choices of others by offering undesirable alternatives,
Exercise 7.80 (p. 394). In another experiment conducted by
the researcher, 96 subjects were asked to imagine that they
t
had just moved to an apartment with two others and that
they were shopping for a new appliance (e.g., television,
microwave oven). Each subject was asked to create a menu
of three brand choices for their roommates; then subjects
were randomly assigned (in equal numbers) to one of three
different “goal” conditions-(1) create the menu in order to
influence roommates to buy a preselected brand, (2) create
the menu in order to influence roommates to buy a brand
of your choice, and (3) create the menu with no intent to
influence roommates. The researcher theorized that the
menus created to influence others would likely include undesirable alternative brands. Consequently, the number of
menus in each goal condition that was consistent with the
theory was determined. The data are summarized in the
table below. Analyze the data for the purpose of determining whether the proportion of subjects who selected menus
consistent with the theory depends on goal condition.
Use a= .01. \ :> = ·1 2.47
Goal Condition
Influence/preselected
brand
Influence/own brand
No influence
,…_.—~–~··- — . —
Number
Consistent
with Theory
Number Not
Consistent
with Theory
15
17
18
14
3
29
Totals
32
32
32
Source: Based on Hamilton. R. W. ·’Why do people suggest what they do not
want? Using context effects to influence others · choices.” Jo11rn a/ of Consumer
Research, Vol. 29. No. 4, March 2003 (Table 2).
Applying the Concepts- Basic
10.40 Location of major sports venues. There has been a trend
0 for professional sports franchises to build new stadiums
VENUES and ballparks in urban, downtown venues. An article in
Professional Geographer (Feb. 2000) investigated whether
there has been a significant suburban-to-urban shift in the
location of major sports facilities. In 1985, 40% of all major
sports facilities were located downtown, 30% in a central
city, and 30% in suburban areas. In contrast, of the 113
major sports franchises that existed in 1997, 58 were built
downtown, 26 in a central city, and 29 in a suburban area.
a. Describe the qualitative variable of interest in the study.
Give the levels (categories) associated with the variable.
b. Give the null hypothesis for a test to determine whether
the proportions of major sports facilities in downtown,
central city, and suburban areas in 1997 were the same
as in 1985. If : p
.•HJ. p
‘.3tJ . )
::iu
c. If the null hypothesis, part b, is true, how many of the
113 sports fa cilities in 1997 would you expect to be
located in downtown, central city, and suburban areas,
. 1y.?