Business Statistics MGT 233, Spring 2015
Homework #3
This homework assignment is due at the beginning of class on April 3, 2015.
Instructions: Download the MGT 233 Homework 3 Excel Data.xlsx from the MGT 233 website. Use the
appropriate table to create the Excel Descriptive statistics. You must print the output of the descriptive statistics
as part of your homework. Answer all parts clearly with proper probability notation and interpretation.
Problem 1
Bookit.com—Bookit.com is an online travel company determined and dedicated
to becoming the leader in providing travelers with the most intuitive online
booking experience full of relevant information, helpful guides and travel tips.
Below is a list of prices for spring break hotel rates. The rate listed below is a
nightly rate. Assume that prices are normally distributed:
Location
Hotel Rate
Panama City -Seahaven
174
Panama City -Palms Resort
189
Panama City -Beach Resort
256
Cancun -Barcelo Costa
106
Cancun - Oasis
115
Cancun -Hyatt Regency
91
Daytona Beach -Plaza
106
Daytona Beach -Mayan Inn
151
Daytona Beach -La Playa Resort
84
New Orleans -Wyndham Riverfront
379
New Orleans -Ramada Plaza
255
New Orleans -Maison Dupuy Hotel
324
Miami -Royal Palm Hotel
430
Miami -Carlton Hotel
299
Miami -Whitelaw Hotel
369
Fort Lauderdale -Beach Resort
170
Fort Lauderdale -Sea Club Resort
205
Fort Lauderdale -Hollywood Beach Resort
155
Print the descriptive statistics in Excel and use the information to complete this problem.
a) Compute and interpret the 90% confidence level for the average price of a night stay at a hotel during
spring break. Interpret the results.
b) Compute and interpret the 95% confidence level for the average price of a night stay at a hotel during
spring break. Interpret the results.
c) Compute and interpret the 99% confidence level for the average price of a night stay at a hotel during
spring break. Interpret the results.
Problem 2
ESPN.com—The average age of starting quarterbacks has been
falling the past two years thanks to good, young passers such as Matt
Ryan, Joe Flacco, Sam Bradford, Josh Freeman and others. In 2009
and 2010, the average age of starters was 28.3, down from 29.1 in
2008.
Below is a random list of some of the 2011 quarterbacks in the NFL.
Name
Age
Name
Age
Name
Age
Name
Age
Kaepernick, Colin
24
Orton, Kyle
29
O'Connell, Kevin
26
Grossman, Rex
31
Smith, Alex
27
Palko, Tyler
28
Sanchez, Mark
25
Brees, Drew
33
Tolzien, Scott
24
Stanzi, Ricky
24
Hill, Shaun
32
Canfield, Sean
25
Cutler, Jay
28
Collins, Kerry
39
Stafford, Matthew
24
Daniel, Chase
25
Enderle, Nathan
24
Manning, Peyton
35
Stanton, Drew
27
Jackson, Tarvaris
28
Hanie, Caleb
26
Orlovsky, Dan
28
Flynn, Matt
26
Lee, Zac
24
McCown, Josh
32
Painter, Curtis
26
Harrell, Graham
26
Portis, Josh
24
Dalton, Andy
24
Greisen, Chris
35
Hill, Nick
26
Whitehurst, Charlie
29
Gradkowski, Bruce
29
McGee, Stephen
25
Rodgers, Aaron
28
Batch, Charlie
37
Robinson, Zac
25
Romo, Tony
31
Anderson, Derek
28
Dixon, Dennis
27
Fitzpatrick, Ryan
29
Devlin, Pat
23
Clausen, Jimmy
24
Johnson, Jerrod
23
Thigpen, Tyler
27
Henne, Chad
26
Newton, Cam
22
Leftwich, Byron
32
Lewis, Thaddeus
24
Losman, J.P.
30
Brady, Tom
34
Roethlisberger, Ben
30
McCoy, Colt
25
Moore, Matt
27
Hartline, Mike
23
Smith, Troy
27
Wallace, Seneca
31
Edwards, Trent
28
Hoyer, Brian
26
Delhomme, Jake
37
Quinn, Brady
27
Kafka, Mike
24
Mallett, Ryan
23
Garcia, Jeff
42
Tebow, Tim
24
Vick, Michael
31
Boller, Kyle
30
Leinart, Matt
28
Weber, Adam
24
Young, Vince
28
Bomar, Rhett
26
Schaub, Matt
30
Carpenter, Rudy
25
Redman, Chris
34
Campbell, Jason
30
Yates, T.J.
24
Freeman, Josh
24
Ryan, Matt
26
Palmer, Carson
32
Hasselbeck, Matt
36
Johnson, Josh
25
Wilson, John Parker
26
Pryor, Terrelle
22
Locker, Jake
23
Ratliff, Brett
26
Carr, David
32
Bradford, Sam
24
Smith, Rusty
25
Bartel, Richard
29
Manning, Eli
31
Brandstater, Tom
27
Bethel-Thompson, McLeod
23
Hall, Max
26
Perrilloux, Ryan
25
Clemens, Kellen
28
Ponder, Christian
24
Kolb, Kevin
27
Gabbert, Blaine
22
Feeley, A.J.
34
Rosenfels, Sage
34
Skelton, John
23
LeFevour, Dan
24
Flacco, Joe
27
Webb, Joe
25
Rivers, Philip
30
McCown, Luke
30
Taylor, Tyrod
22
Volek, Billy
35
Brunell, Mark
41
Beck, John
30
Cassel, Matt
29
McElroy, Greg
23
Crompton, Jonathan
24
Print the descriptive statistics in Excel and use the information to complete this problem.
a) With 95% confidence interval, what is the margin of error?
b) What is the 95% confidence interval estimate for the mean age of NFL quarterbacks? Interpret your
results.
c) What is the 99% confidence interval estimate for the mean age of NFL quarterbacks? Interpret your
results.
Problem 3
Teamrankings.com— Looking at MLB teams, the average number of
team runs per games varies for each team. During the 2012 season, the
Texas Rangers lead the league with 4.96 per game followed by the NY
Yankees with 4.83. Below is a table random sample of some MLB teams
“runs per game”. Assume that the average team runs per game is
normally distributed.
Team
2012
Philadelphia
4.22
Washington
4.47
Chi Cubs
3.78
Colorado
4.68
Cincinnati
4.14
Toronto
4.42
Pittsburgh
4.02
LA Dodgers
3.93
San Diego
4.02
Arizona
4.53
Texas
4.96
Kansas City
4.17
Detroit
4.40
Boston
4.53
Answer the following questions using calculations by hand (without using Excel). Show the equations and
summations need for the calculations. Round all work to three decimal points.
a) Compute the standard deviation for the mean runs per game.
b) At 99% confidence, what is the margin of error?
c) What is the 99% confidence interval for the average runs per game for MLB teams? Interpret the results.
Problem 4
iFly.com-- The Transportation Security Administration (TSA) urges all
travelers to arrive at the airport well in advance of scheduled flight
departures and has provided security checkpoint wait time information
as a guide to assist in travel planning. You must also check airlines for
ticket counter wait times as well as possible changes to flight
schedules.
According to historical averages reported by the TSA, at the Omaha Eppley Airfield Airport (OMA), security
wait times vary depending on the time of your flight. At 6 AM the average wait time for concourse A is 9.5
minutes while the maximum wait reported is 17 minutes. The population standard deviation is 2.33 minutes. At
6 AM the average wait time for concourse B is 7 minutes while the maximum wait reported is 11 minutes. The
population standard deviation is 1.87 minutes.
Assuming 80% confidence, what is the sample size that TSA should use to obtain a margin of error of
30 seconds for concourse A?
b) Assuming 90% confidence, what is the sample size that TSA should use to obtain a margin of error of
15 seconds concourse B?
a)
Problem 5
RIP Rating.com--The average NBA player at the start of the 2010-11 season was 26.77
years old and had 4.84 years of NBA experience. Player turnover in the NBA is fast and
furious, and you need only look at the roster of your favorite NBA team and compare it to
last year to understand this fact. Only exceptional talent lasts in the NBA for any length
of time. Shaquille O'Neal of the Boston Celtics was the elder statesman of the NBA this
season.
Looking at the Boston Celtics roaster the ages of the players vary. Below is the 2010-11
roster for the Boston Celtics. Assume that number of years the players and coach have
been in the NBA are normally distributed:
Years in
PLAYER
the NBA
Ray Allen
16
Carlos Arroyo
10
Avery Bradley
2
Glen Davis
5
Kevin Garnett
17
Jeff Green
5
JaJuan Johnson
1
Nenad Krstic
8
E'Twaun Moore
1
Troy Murphy
11
Jermaine O'Neal
16
Aleksandar Pavlovic
9
Paul Pierce
14
Rajon Rondo
6
Von Wafer
7
Delonte West
8
Doc Rivers
5
Answer the following questions using Excel descriptive statistics.
a) At 80% confidence, what is the margin of error?
b) What is the 80% confidence interval for the estimated number of years played in the NBA by a Celtic
player? Interpret the results.
Problem 6
FOXNEWS.COM, March 11, 2013
NY judge halts Bloomberg ban on large sugary drinks
A New York judge is forcing the Bloomberg administration to take a
big gulp -- striking down its groundbreaking and controversial limit
on the size of sugary drinks in New York City shortly before it was set
to take effect.
Manhattan state Supreme Court Justice Milton Tingling wrote in his opinion that the rules are "arbitrary and
capricious," applying to only certain beverages and only certain stores. "The loopholes in this rule effectively
defeat the stated purpose of this rule," he wrote, complaining of "uneven enforcement even within a particular
City block, much less the City as a whole."
New York City Mayor Michael Bloomberg plans to appeal, his office said on Twitter shortly after the ruling.
"We believe (the city) has the legal authority and responsibility to tackle causes of the obesity epidemic, which
kills 5,000 NYers a year," his office said, voicing confidence that the measure would be upheld.
But Tingling said the city's Board of Health went beyond its authority, and effectively would be "limited by its
own imagination" if left unchecked. "The portion cap rule, if upheld, would create an administrative Leviathan
and violate the separation of powers doctrine," by straying into territory that should belong to the elected City
Council, not the board appointed by Mayor Michael Bloomberg, Tingling wrote. That, he wrote, "has the
potential to be more troubling than sweetened beverages.
A survey was performed recently by the organization the SPUNK (Student Perspectives at UNK). It surveyed
students that were informed and had an opinion whether the judge was correct in removing the limit on the size
of sugary drinks in New York City. SPUNK as these students, “Do you believe the judge was correct in
removing the limit on the size of sugary drinks in New York City?” Of the 124 informed students that were
surveyed and had an opinion, 93 said yes, 31 said no.
a) Construct and interpret an 80% confidence interval for the proportion of informed UNK students that
believe the judge was correct in removing the limit on the size of sugary drinks in New York City.
b) Construct and interpret a 99% confidence interval for the proportion of informed UNK students believe
the judge was correct in removing the limit on the size of sugary drinks in New York City.
Problem 7
A UNK education is excellent preparation for a successful career,
and nowwhere is this more evident than at the annual Career Fair
when employers from across the state gather together at the
Health and Sports Center to meet, greet and recruit UNK
graduate.
The Organizer of UNK Career fair took a sample of 60 UNK
graduates to check whether they were planning to attend the
Career Fair, Half of the students indicated they plan to attend this
event. With 80% confidence, the organizer claims that the survey has a margin of error of plus or minus 8.2
percentage points.
a) Was the organizer of the Career Fair accurate in reporting a margin of error of 8.2 Percent? Show work
by caring the answer to 4 decimal places.
b) What sample size is needed for a margin of error of 5 percent with 90 percent confident?
c) What sample size is needed for a margin of error of 3 percent with 95 percent confident?
d) What sample size is needed for a margin of error of 1 percent with 98 percent confident?
Problem 8
Businessweek.com--How did the U.S. become the world's largest
economy? A key part of the answer is education. Some 85% of adult
Americans have at least a high school degree today, up from just 25% in
1940. Similarly, 28% have a college degree, a fivefold gain over this
period. Today's U.S. workforce is the most educated in the world.
The above information was found in 2005. You are asked to complete a
survey to obtain more current information.
a) What sample size would you want to use to estimate the current proportion of individuals who now have
a high school degree with a 2% margin of error? Use a 99% confidence level.
b) What sample size would you want to use to estimate the current proportion of individuals who now have
a college degree with a 5% margin of error? Use a 95% confidence level.
Problem 9
Usaswimming.org—The 2012 U.S. Olympic Team Trials Swimming will return June 25-July 2 to Omaha, Nebraska, as one
of the fastest, exciting, suspenseful and pressure-filled competitions
held in the United States every four years. Check back often for
updates as we draw closer to naming the team that will represent
the United States in the pool at the London Olympic Games.
Looking back at the 2012 Olympic Team Trials, swimmers swam
in qualifying heats, semi-final heats, and finals event. Sixteen
swimmers made it to the semi-finals and eight swimmers competed in the finals in order to make the USA
Olympic team. A random sample of the top swimmers from the first round of heats was taken. A sample of 50
men’s 100m freestyle swimmers shows an average time of 49.68 seconds and a standard deviation of 0.73
seconds. While a sample of 47 men’s 100m butterfly swimmers shows an average time of 53.69 seconds and a
standard deviation of 0.76 seconds.
a) What is the point estimate of the difference between the mean 100m butterfly times and the mean 100m
freestyle times?
b) Is the 90% confidence interval for the difference between the average 100m butterfly and 100m freestyle
times? Interpret the results.
c) Suppose, you want to estimate the average Women’s 100m butterfly time with a new survey.
Historically, the standard deviation of times for the Women’s 100m butterfly is about the same as the
Men’s 100m butterfly. If you want a 95% confidence and a margin of error within 0.20 seconds, what
sample size do you need?
Problem 10
Yahoo! Finance (March 4, 2013)--Microsoft Corporation will launch the latest version of its tablet Surface, Surface RT
with Windows RT in Japan, Mexico, New Zealand, Russia, Singapore and Taiwan. Further, it will launch its Surface Pro
with Windows 8 Pro in Australia, China, France, Germany, Hong Kong, New Zealand and the United Kingdom in March.
Microsoft is very bullish about its tablet and is rapidly strengthening its global
retail presence. Microsoft is a late entrant into the tablet market and beating the
competition at this point will be an uphill task. Other successful tablets such as
Apple’s iPads, Google’s Nexus 7, Samsung’s Galaxy tablets and Amazon’s
Kindle Fire already have a strong presence in the market.
Suppose a follow up survey was performed to compare Nebraska
consumers to New York consumers. Out of the 112 Nebraskans
surveyed, 84 said they would pick the Surface RT over the iPad.
Likewise, 130 individuals from New York were surveyed with 78
preferring the Surface RT.
a) Compute the 95% confidence interval for the difference between the proportions of individuals from
Nebraska verse New York that would choose the Surface RT over the iPad. Interpret your results.