Business Statistics, MGT 233

Homework #3, Fall 2012

Instructions: Download the Homework 3 Excel Data.xlsx file from the MGT 233 web site. 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 Christmas vacation 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.

Hotel Rate

Mean 214.3333333

Standard Error 25.40675634

Median 181.5

Mode 106

Standard Deviation 107.7917382

Sample Variance 11619.05882

Kurtosis -0.755842257

Skewness 0.634889446

Range 346

Minimum 84

Maximum 430

Sum 3858

Count 18

a) Compute and interpret the 90% confidence level for the average price of a night

stay at a hotel during Christmas vacation. Interpret the results.

( )

We are 90% confident that the average price of a hotel for

Christmas vacation will be between $170.13 and $258.54.

+3

+2

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b) Compute and interpret the 95% confidence level for the average price of a night stay at a

hotel during Christmas vacation. Interpret the results.

( )

We are 95% confident that average price of a hotel for

Christmas vacation will be between $160.73 and $267.94.

c) Compute and interpret the 99% confidence level for the average price of a night stay at a

hotel during Christmas vacation. Interpret the results.

( )

We are 99% confident that average price of a hotel for

Christmas vacation will be between $140.70 and $287.96.

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+2

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+2

Problem 2

Answers.com—When counting only quarterbacks

that have played more than a full year in the NFL,

you would be amazed at how many short-lived

quarterbacks there have been. The average career

length of an NFL quarterback is 6.6 years.

Below is a list of NFL quarterbacks and the

number of years of experience each of them have.

Assume the number of years of experience for the

NFL quarterbacks is normally distributed.

Name Years Name Years Name Years Name Years

Kaepernick, Colin 0 Orton, Kyle 7 O'Connell, Kevin 4 Grossman, Rex 9

Smith, Alex 7 Palko, Tyler 1 Sanchez, Mark 3 Brees, Drew 11

Tolzien, Scott 0 Stanzi, Ricky 0 Hill, Shaun 10 Canfield, Sean 1

Cutler, Jay 6 Collins, Kerry 17 Stafford, Matthew 3 Daniel, Chase 3

Enderle, Nathan 0 Manning, Peyton 14 Stanton, Drew 5 Jackson, Tarvaris 6

Hanie, Caleb 4 Orlovsky, Dan 7 Flynn, Matt 4 Lee, Zac 0

McCown, Josh 9 Painter, Curtis 3 Harrell, Graham 1 Portis, Josh 0

Dalton, Andy 0 Greisen, Chris 3 Hill, Nick 0 Whitehurst, Charlie 6

Gradkowski, Bruce 6 McGee, Stephen 3 Rodgers, Aaron 7 Batch, Charlie 14

Robinson, Zac 2 Romo, Tony 9 Anderson, Derek 6 Dixon, Dennis 4

Fitzpatrick, Ryan 7 Devlin, Pat 0 Clausen, Jimmy 2 Johnson, Jerrod 0

Thigpen, Tyler 5 Henne, Chad 4 Newton, Cam 0 Leftwich, Byron 9

Lewis, Thaddeus 1 Losman, J.P. 7 Brady, Tom 12 Roethlisberger, Ben 8

McCoy, Colt 2 Moore, Matt 5 Hartline, Mike 0 Smith, Troy 5

Wallace, Seneca 9 Edwards, Trent 5 Hoyer, Brian 3 Delhomme, Jake 13

Quinn, Brady 5 Kafka, Mike 2 Mallett, Ryan 0 Garcia, Jeff 12

Tebow, Tim 2 Vick, Michael 10 Boller, Kyle 8 Leinart, Matt 6

Weber, Adam 0 Young, Vince 6 Bomar, Rhett 2 Schaub, Matt 8

Carpenter, Rudy 3 Redman, Chris 9 Campbell, Jason 7 Yates, T.J. 0

Freeman, Josh 3 Ryan, Matt 4 Palmer, Carson 9 Hasselbeck, Matt 13

Johnson, Josh 4 Wilson, John Parker 3 Pryor, Terrelle 0 Locker, Jake 0

Ratliff, Brett 4 Carr, David 10 Bradford, Sam 2 Smith, Rusty 2

Bartel, Richard 3 Manning, Eli 8 Brandstater, Tom 2 Bethel-Thompson, McLeod 0

Hall, Max 2 Perrilloux, Ryan 1 Clemens, Kellen 6 Ponder, Christian 0

Kolb, Kevin 5 Gabbert, Blaine 0 Feeley, A.J. 11 Rosenfels, Sage 11

Skelton, John 2 LeFevour, Dan 2 Flacco, Joe 4 Webb, Joe 2

Rivers, Philip 8 McCown, Luke 8 Taylor, Tyrod 0

Volek, Billy 12 Brunell, Mark 19 Beck, John 5

Cassel, Matt 7 McElroy, Greg 0 Crompton, Jonathan 1

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 number of experience for an NFL

quarterback? Interpret your results.

( )

We are 95% confident that the average experience of NFL

quarterbacks is between 3 years 9 months and 6 years 5

months.

+1 +2

+2

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Mean 5.0833

Standard Error 0.6663

Median 4

Mode 0

Standard Deviation 4.6165

Sample Variance 21.3121

Kurtosis 0.9613

Skewness 1.0925

Range 19

Minimum 0

Maximum 19

Sum 244

Count 48

Years

+3

c) What is the 99% confidence interval estimate for the mean number of experience for an NFL

quarterback? Interpret your results.

( )

We are 99% confident that the average experience of NFL

quarterbacks is between 3 years 4 months and 5 years 10

months.

+2

+2

+2

Problem 3

Teamrankings.com—Looking at MLB teams, the average

number of team runs per games varies for each team.

During the 2011 season, the Boston Red Sox lead the league

with 5.4 per game followed by the Yankees with 5.36.

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 2011

Boston 5.4

NY Yankees 5.36

Texas 5.27

Detroit 4.79

St. Louis 4.78

Toronto 4.59

Cincinnati 4.54

Colorado 4.54

Arizona 4.53

Kansas City 4.51

Milwaukee 4.45

NY Mets 4.43

Philadelphia 4.4

Tampa Bay 4.39

Baltimore 4.37

Cleveland 4.35

LA Angels 4.12

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.

∑

(∑ )

( )

( )

( )

√ runs

b) At 99% confidence, what is the margin of error?

√

√

+4

+2

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c) What is the 99% confidence interval for the average runs per game for MLB teams? Interpret

the results.

( )

We are 99% confident that on average teams have between 4.303

and 4.859 runs per game.

+2

+2

+1

+1

Problem 4

WildAboutMovies.com—Sequels had a huge presence on the big screen in

2011. The biggest success at the 2011 movie box office was the final and

eighth Harry Potter version (until the remakes come along in 20 years or

so).

The year was full of sequels. In fact, the Top 10 Movie at the 2011 Movie

Box Office, were sequels, remakes, reboots or first installments of impending

sequels.

Below is a random sample of movies and their total gross revenue

Title Total Gross Title Total Gross

50/50 $35,014,192 Scream 4 $38,180,928

Captain America: The First Avenger $176,654,505 Source Code $54,712,227

Cars 2 $191,452,396 Spy Kids: All the Time in the World $38,538,188

Crazy, Stupid, Love. $84,351,197 Super 8 $127,004,179

Diary of a Wimpy Kid: Rodrick Rules $52,698,535 The Adjustment Bureau $62,495,645

Fast Five $209,837,675 The Descendants $80,589,274

Final Destination 5 $42,587,643 The Help $169,705,587

Green Lantern $116,601,172 The Lincoln Lawyer $58,009,200

Horrible Bosses $117,538,559 The Muppets $88,479,901

Jack and Jill $74,158,157 The Rite $33,047,633

Just Go With It $103,028,109 The Roommate $37,300,107

Larry Crowne $35,608,245 The Twilight Saga: Breaking Dawn Part 1$281,287,133

Moneyball $75,605,492 Thor $181,030,624

New Year's Eve $54,544,638 Tower Heist $78,046,570

Paranormal Activity 3 $104,028,807 War Horse $79,237,317

Priest $29,136,626 We Bought a Zoo $74,444,931

Rango $123,477,607 Zookeeper $80,360,843

Print the descriptive statistics in Excel and use the information to complete this problem.

Mean 93,788,054

Standard Error 10,227,554

Median 78,641,944

Mode #N/A

Standard Deviation 59,636,377

Sample Variance 3,556,497,488,635,270

Kurtosis 1.7370

Skewness 1.3659

Range 252,150,507

Minimum 29,136,626

Maximum 281,287,133

Sum 3,188,793,842

Count 34

Total Gross

a) What is the 80% confidence interval estimate for the mean total gross for a box office movie?

( )

We are 80% confident that the average revenue for a box office

movie is between and

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b) What is the 90% confidence interval estimate for the mean total gross for a box office movie?

( )

We are 90% confident that the average revenue for a box office

movie is between and .

c) What is the 95% confidence interval estimate for the mean total gross for a box office movie?

( )

We are 95% confident that the average revenue for a box office

movie was between and .

+2

+2

+2

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Problem 5

Cincinnati.com, October 28, 2012 - Ohio poll: Tight race now even tighter

Our ongoing poll shows the president's numbers have shrunk, as Romney and Obama draw dead

even among Ohio's likely voters. A late surge by Mitt Romney has made the contest between him

and President Obama to win Ohio too close to call, according to a poll released Sunday. Romney and

Obama appear tied at 49 percent among likely voters, according to an Ohio News Organization poll

a) You are the one of the official fact checker for the student paper The Antelope. Was the

University of Cincinnati’s Institute for Policy Research accurate in reporting a margin of

error of 3.1 percent at 95% confidence? Show work by caring you work to 4 decimal places.

√

, yes it is correct.

+3

b) What sample size is needed for a margin of error of 3 percent with 98 percent confidence?

( )

c) What sample size is needed for a margin of error of 2 percent with 98 percent confidence?

( )

d) What sample size is needed for a margin of error of 1 percent with 99 percent confidence?

( )

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Problem 6

FOXNEWS.COM, October 30, 2012, Lt. Col. Tony Shaffer (ret.)

To live and die in Benghazi, Libya without leadership from America

What is it like to spend your last moments on earth fighting for

your life?

To have devoted your life, and your life's work, to a great

nation -- to serve it well and honorably -- and serve for it

with courage and distinction, to all come down to a last,

frantic few seconds, spent defending you and your fellow

Americans and call for the cavalry to come help, and no

cavalry comes--and you die. This is what the two former

Navy SEALs, under the employment of CIA, Tyrone Woods

and Glen Doherty, faced in their final moments in

Benghazi on September 11, 2012.

It is not a question of could we have sent forces in to help. We could. We could have sent forces to help as

they were within a few hundred miles. This battle of Benghazi was a protracted fight - covering at least six to

eight hours (depending on when you start the clock). And, if the forces were not there, on the anniversary of

the 9/11 attacks, then there is an additional level of leadership failure that must be examined. However, the

appearance is that there were forces available.

Is what we now stand for now, as a nation? To have invested billions in intelligence and special operations

forces to hang back, play it safe? … The request for help was sent by these brave, now dead, men - at least

three times. The answer was "no". Someone made the decision to not send help. Who?

Read more: http://www.foxnews.com/opinion/2012/10/30/to-live-and-die-in-benghazi-libya-

without-leadership-from-america

A survey was performed recently an organization call SPUNK (Student Perspectives at UNK). It

surveyed students that were informed and had an opinion whether this story will have an impact in

the election results. SPUNK as these students, “Do you want to know, before the presidential

election, who made the decision to not send help” 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 want to know, before the presidential election, who made the decision to not

send help.

√

( )

SPUNK is 80% confident that between 70% to 80% of

informed UNK students that want to know, before the

presidential election, who made the decision to not send help.

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b) Construct and interpret a 99% confidence interval for the proportion of informed UNK

students that want to know, before the presidential election, who made the decision to not

send help.

√

( )

SPUNK is 99% confident that between 65% to 85% of informed

UNK students that want to know, before the presidential

election, who made the decision to not send help.

+2

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Problem 7

Usgovinfo.about.com—Nearly 47 million

people -- about 1-in-5 U.S. residents --

age 5 and older, reported regularly

speaking a foreign language at home in

2000, according to the Census Bureau. The

figures represented an increase of 15

million people since the 1990 census.

The new census report, Language Use and

English-Speaking Ability: 2000, (PDF) said 55 percent of the people who spoke a language other

than English at home also reported they spoke English "very well." Combined with those who spoke

only English at home, 92 percent of the population age 5 and over had no difficulty speaking

English.

Since the above information was from 2000, you are asked to complete a survey to obtain more

current information on the number of Americans who’s second language is English.

a) What sample size would you want to use to estimate the current proportion of individuals who

regularly speak a foreign language at home 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

regularly speak a foreign language at home with a 5% margin of error? Use a 95%

confidence level.

( )

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+3

Problem 8

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.

√

√

.1515 seconds

( )

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?

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Problem 9

Getamericafit.org—Obesity is the #2 cause of preventable death in

the United States. 60 million Americans that are 20 years and older

are obese. 9 million children and teens ages 6-19 are overweight.

Being overweight or obese increases the risk of health conditions and

diseases including: Breast cancer, Coronary heart disease, Type II

diabetes, Sleep apnea, Gallbladder disease, Osteoarthritis, Colon

cancer, Hypertension and Stroke.

According to a sample done by the ‘Get America Fit Foundation,’ in

2008, obesity prevalence was highest among American Indian or Alaska Native children (21.2%

of the 214 American Indian or Alaska Native children sampled) and lowest among white

children (12.6% of the 305 white children sampled

Compute the 95% confidence interval for the difference between the proportions of American

Indian children that are obese verse the white children that are obese. Interpret your results.

√ ( )

( )

√

( )

( )

Get America Fit is 95% confident that 2% to 15.2% more

American Indian children that are obese than white children.

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