Chapter 3, Descriptive Statistics: Numerical Measures Video Solutions, Essentials of Statistics for Business & Economics | Numerade (2024)

eICU Waiting Times. There is a severe shortage of critical care doctors and nurses to provide intensive-care services in hospitals. To offset this shortage, many hospitals, such as Emory Hospital in Atlanta, are using electronic intensive-care units (eICUs) to help provide this care to patients (Emory University News Center), elCUs use electronic monitoring took and twoway communication through video and audio so that a centralized staff of specially trained doctors and nurses-who can be located as far away as Australia-can provide critical care services to patients located in remote hospitals without fully staffed ICUs. One of the most important metrics tracked by these eICUs is the time that a patient must wait for the first video interaction between the patient and the eICU staff. Consider the following sample of 40 patient waiting times until their first video interaction with the eICU staff.

$$
\begin{array}{cccc}
\begin{array}{c}
\text { Wait Time } \\
\text { (minutes) }
\end{array} & \begin{array}{c}
\text { Wait Time } \\
\text { (minutes) }
\end{array} & \begin{array}{c}
\text { Wait Time } \\
\text { (minutes) }
\end{array} & \begin{array}{l}
\text { Wait Time } \\
\text { (minutes) }
\end{array} \\
40 & 46 & 49 & 44 \\
45 & 45 & 38 & 51 \\
42 & 46 & 41 & 45 \\
49 & 41 & 48 & 42 \\
49 & 40 & 42 & 43 \\
43 & 42 & 41 & 41 \\
55 & 43 & 42 & 40 \\
42 & 40 & 49 & 43 \\
44 & 45 & 61 & 37 \\
40 & 37 & 39 & 43
\end{array}
$$

a. Compute the mean waiting time for these 40 patients.
b. Compare the mean waiting time.
c. Compute the mode.
d. Compute the first and third quartiles.

Advertising Spending. Which companies spend the most money on advertising?
Business Insider maintains a list of the top-spending companies. In 2014, Procter & Gamble spent more than any other company, a whopping $$\$ 5$$ billion. In second place was Comcast, which spent $$\$ 3.08$$ billion (Business Insider website). The top 12 companies and the amount each spent on advertising in billions of dollars are as follows.

$$
\begin{array}{lclc}
\text { Company } & \begin{array}{l}
\text { Advertising } \\
\text { (\$billions) }
\end{array} & \text { Company } & \begin{array}{c}
\text { Advertising } \\
\text { (\$billions) }
\end{array} \\
\text { Procter \& Gamble } & \$ 5.00 & \text { American Express } & \$ 2.19 \\
\text { Comcast } & 3.08 & \text { General Motors } & 2.15 \\
\text { AT\&T } & 2.91 & \text { Toyota } & 2.09 \\
\text { Ford } & 2.56 & \text { Fiat Chrysler } & 1.97 \\
\text { Verizon } & 2.44 & \text { Walt Disney Company } & 1.96 \\
\text { L'Oreal } & 2.34 & \text { J.P. Morgan } & 1.88
\end{array}
$$
a. What is the mean amount spent on advertising?
b. What is the median amount spent on advertising?
c. What are the first and third quartiles?

Time Spent Watching Traditional TV. Nielsen tracks the amount of time that people spend consuming media content across different platforms (digital, audio, television) in the United States. Nielsen has found that traditional television viewing habits vary based on the age of the consumer as an increasing number of people consume media through streaming devices (Nielsen website). The following data represent the weekly traditional TV viewing hours in 2016 for a sample of 14 people aged $18-34$ and 12 people aged $35-49$.
$$
\begin{array}{ll}
\text { Viewers aged } & 18-34: 24.2,21.0,17.8,19.6,23.4,19.1,14.6,27.1,19.2,18.3, \\
& 22.9,23.4,17.3,20.5 \\
\text { Viewers aged } & 35-49: 24.9,34.9,35.8,31.9,35.4,29.9,30.9,36.7,36.2,33.8, \\
& 29.5,30.8
\end{array}
$$

a. Compute the mean and median weekly hours of traditional TV viewed by those aged $18-34$.
b. Compute the mean and median weekly hours of traditional TV viewed by those aged $35-49$.
c. Compare the mean and median viewing hours for each age group. Which group watches more traditional TV per week?

Online Multiplayer Game Downloads. The creator of a new online multiplayer survival game has been tracking the monthly downloads of the newest game. The following table shows the monthly downloads (in thousands) for each month of the current and previous year.

$$
\begin{array}{lclc}
\begin{array}{lcc}
\text { Month } \\
\text { (previous year) }
\end{array} & \begin{array}{c}
\text { Downloads } \\
\text { (thousands) }
\end{array} & \begin{array}{l}
\text { Month } \\
\text { (current year) }
\end{array} & \begin{array}{c}
\text { Downloads } \\
\text { (thousands) }
\end{array} \\
\text { February } & 33.0 & \text { January } & 37.0 \\
\text { March } & 34.0 & \text { February } & 37.0 \\
\text { April } & 34.0 & \text { March } & 37.0 \\
\text { May } & 32.0 & \text { April } & 38.0 \\
\text { June } & 32.0 & \text { May } & 37.0 \\
\text { July } & 35.0 & \text { June } & 36.0 \\
\text { August } & 34.0 & \text { July } & 37.0 \\
\text { September } & 37.0 & \text { August } & 35.0 \\
\text { October } & 37.0 & \text { September } & 33.0 \\
\text { November } & 35.0 & \text { October } & 32.0 \\
\text { December } & 33.0 & &
\end{array}
$$

a. Compute the mean, median, and mode for number of downloads in the previous year.
b. Compute the mean, median, and mode for number of downloads in the current year.
c. Compute the first and third quartiles for downloads in the previous year.
d. Compute the first and third quartiles for downloads in the current year.
e. Compare the values calculated in parts a through d for the previous and current years. What does this tell you about the downloads of the game in the current year compared to the previous year?

Motor Oil Prices. Martinez Auto Supplies has retail stores located in eight cities in California. The price they charge for a particular product in each city varies because of differing competitive conditions. For instance, the price they charge for a case of a popular brand of motor oil in each city follows. Also shown are the number of cases that Martinez Auto sold last quarter in each city.

$$
\begin{array}{lcc}
\text { City } & \text { Price (\$) } & \text { Sales (cases) } \\
\text { Bakersfield } & 34.99 & 501 \\
\text { Los Angeles } & 38.99 & 1425 \\
\text { Modesto } & 36.00 & 294 \\
\text { Oakland } & 33.59 & 882 \\
\text { Sacramento } & 40.99 & 715 \\
\text { San Diego } & 38.59 & 1088 \\
\text { San Francisco } & 39.59 & 1644 \\
\text { San Jose } & 37.99 & 819 \\
& &
\end{array}
$$
Compute the average sales price per case for this product during the last quarter.

Mutual Fund Rate of Return. The following table shows the total return and the number of funds for four categories of mutual funds.
$$
\begin{array}{lcc}
\text { Type of Fund } & \text { Number of Funds } & \text { Total Return (\%) } \\
\text { Domestic Equity } & 9191 & 4.65 \\
\text { Intornational Equity } & 2621 & 18.15 \\
\text { Specialty Stock } & 1419 & 11.36 \\
\text { Hybrid } & 2900 & 6.75
\end{array}
$$

a. Using the number of funds as weights, compute the weighted average total return for these mutual funds.
b. Is there any difficulty associated with using the "number of funds" as the weights in computing the weighted average total return in part (a)? Discuss. What else might be used for weights?
c. Suppose you invested $$\$ 10,000$$ in this group of mutual funds and diversified the investment by placing $$\$ 2000$$ in Domestic Equity funds, $$\$ 4000$$ in International Equity funds, $$\$ 3000$$ in Specialty Stock funds, and $$\$ 1000$$ in Hybrid funds. What is the expected return on the portfolio?

Business School Ranking. Based on a survey of master's programs in business administration, magazines such as U.S. News & World Report rank U.S. business schools. These types of rankings are based in part on surveys of business school deans and corporate recruiters. Each survey respondent is asked to rate the overall academic quality of the master's program on a scale from I "marginal" to 5 "outstanding." Use the sample of responses shown below to compute the weighted mean score for the business school deans and the corporate recruiters. Discuss.

$$
\begin{array}{ccc}
\text { Quality Assessment } & \text { Business School Deans } & \text { Corporate Recruiters } \\
5 & 44 & 31 \\
4 & 66 & 34 \\
3 & 60 & 43 \\
2 & 10 & 12 \\
1 & 0 & 0
\end{array}
$$

Mutual Fund Comparison. Suppose that at the beginning of Year 1 you invested $$\$ 10,000$$ in the Stivers mutual fund and $$\$ 5000$$ in the Trippi mutual fund. The value of each investment at the end of each subsequent year is provided in the table below. Which mutual fund performed better?

$$
\begin{array}{ccr}
\text { Year } & \text { Stivers } & \text { Trippi } \\
1 & 11,000 & 5,600 \\
2 & 12,000 & 6,300 \\
3 & 13,000 & 6,900 \\
4 & 14,000 & 7,600 \\
5 & 15,000 & 8,500 \\
6 & 16,000 & 9,200 \\
7 & 17,000 & 9,900 \\
8 & 18,000 & 10,600
\end{array}
$$

Round-Trip Flight Prices. The following table displays round-trip flight prices from 14 major U.S. cities to Atlanta and Salt Lake City.

$$
\begin{array}{lcc}
\text { Departure City } & \text { Atlanta } & \text { Salt Lake City } \\
\text { Cincinnati } & 340.10 & 570.10 \\
\text { New York } & 321.60 & 354.60 \\
\text { Chicago } & 291.60 & 465.60 \\
\text { Denver } & 339.60 & 219.60 \\
\text { Los Angeles } & 359.60 & 311.60 \\
\text { Seattle } & 384.60 & 297.60 \\
\text { Detroit } & 309.60 & 471.60 \\
\text { Philadelphia } & 415.60 & 618.40 \\
\text { Washington, D.C. } & 293.60 & 513.60 \\
\text { Miami } & 249.60 & 523.20 \\
\text { San Francisco } & 539.60 & 381.60 \\
\text { Las Vegas } & 455.60 & 159.60 \\
\text { Phoenix } & 359.60 & 267.60 \\
\text { Dallas } & 333.90 & 458.60
\end{array}
$$

a. Compute the mean price for a round-trip flight into Atlanta and the mean price for a round-trip flight into Salt Lake City. Is Atlanta less expensive to fly into than Salt Lake City? If so, what could explain this difference?
b. Compute the range, variance, and standard deviation for the two samples. What does this information tell you about the prices for flights into these two cities?

Annual Sales Amounts. Varatta Enterprises sells industrial plumbing valves. The following table lists the annual sales amounts for the different salespeople in the organization for the most recent fiscal year.

$$
\begin{array}{lclc}
\text { Salesperson } & \text { Sales Amount (\$1000) } & \text { Salesperson } & \text { Sales Amount (\$1000) } \\
\text { Joseph } & 147 & \text { Wei } & 465 \\
\text { Jennifer } & 232 & \text { Samantha } & 410 \\
\text { Phillip } & 547 & \text { Erin } & 298 \\
\text { Stanley } & 328 & \text { Dominic } & 321 \\
\text { Luke } & 295 & \text { Charlie } & 190 \\
\text { Lexie } & 194 & \text { Amol } & 211 \\
\text { Margaret } & 368 & \text { Lenisa } & 413
\end{array}
$$

a. Compute the mean, variance, and standard deviation for these annual sales values.
b. In the previous fiscal year, the average annual sales amount was $$\$ 300,000$$ with a standard deviation of $$\$ 95,000$$. Discuss any differences you observe between the annual sales amount in the most recent and previous fiscal years.

Cellular Phone Spending. According to the 2016 Consumer Expenditure Survey, Americans spend an average of $$\$ 1124$$ on cellular phone service annually (U.S. Bureau of Labor Statistics website). Suppose that we wish to determine if there are differences in cellular phone expenditures by age group. Therefore, samples of 10 consumers were selected for three age groups ( $18-34,35-44,45$ and older). The annual expenditure for each person in the sample is provided in the table below.

$$
\begin{array}{ccc}
18-34 & \mathbf{3 5 - 4 4} & \mathbf{4 5} \text { and Older } \\
1355 & 969 & 1135 \\
115 & 434 & 956 \\
1456 & 1792 & 400 \\
2045 & 1500 & 1374 \\
1621 & 1277 & 1244 \\
994 & 1056 & 825 \\
1937 & 1922 & 763 \\
1200 & 1350 & 1192 \\
1567 & 1586 & 1305 \\
1390 & 1415 & 1510
\end{array}
$$

a. Compute the mean, variance, and standard deviation for the each of these three samples.
b. What observations can be made based on these data?

Consistency of Running Times. The following times were recorded by the quarter-mile and mile runners of a university track team (times are in minutes).
$$
\begin{array}{lrrrrr}
\text { Quarter-Mile Times: } & .92 & .98 & 1.04 & .90 & .99 \\
\text { Mile Times: } & 4.52 & 4.35 & 4.60 & 4.70 & 4.50
\end{array}
$$

After viewing this sample of running times, one of the coaches commented that the quarter-milers turned in the more consistent times. Use the standard deviation and the coefficient of variation to summarize the variability in the data. Does the use of the coefficient of variation indicate that the coach's statement should be qualified?

Best Places to Live. Each year Money magazine publishes a list of "Best Places to Live in the United States." These listings are based on affordability, educational performance, convenience, safety, and livability. The list below shows the median household income of Money magazine's top city in each U.S. state for 2017 (Money magazine website).

$$
\begin{array}{|c|c|c|c|}
\hline \text { City } & \begin{array}{l}
\text { Median Household } \\
\text { Income (\$) }
\end{array} & \text { City } & \begin{array}{l}
\text { Median Household } \\
\text { Income (\$) }
\end{array} \\
\hline \text { Pelham, AL } & 66,772 & \text { Bozeman, MT } & 49,303 \\
\hline \text { Juneau, AK } & 84,101 & \text { Papillion, NE } & 79,131 \\
\hline \text { Paradise Valley, AZ } & 138,192 & \text { Sparks, NV } & 54,230 \\
\hline \text { Fayetteville, AR } & 40,835 & \text { Nashua, NH } & 66,872 \\
\hline \text { Monterey Park, CA } & 57,419 & \text { North Adlington, NJ } & 73,885 \\
\hline \text { Lone Tree, CO } & 116,761 & \text { Rio Rancho, NM } & 58,982 \\
\hline \text { Manchester, CT } & 64,828 & \text { Valley Stream, NY } & 88,693 \\
\hline \text { Hockessin, DE } & 115,124 & \text { Concord, NC } & 54,579 \\
\hline \text { St. Augustine, FL } & 47,748 & \text { Dickinson, ND } & 71,866 \\
\hline \text { Vinings, GA } & 73,103 & \text { Wooster, } \mathrm{OH} & 43,054 \\
\hline \text { Kapaa, HI } & 62,546 & \text { Mustang. OK } & 66,714 \\
\hline \text { Meridian, } 10 & 62,899 & \text { Beaverton, OR } & 58,785 \\
\hline \text { Schaumburg, IL } & 73,824 & \text { Lower Merion, PA } & 117,438 \\
\hline \text { Fishers, } \mathbb{I N} & 87,043 & \text { Warwick, RI } & 63,414 \\
\hline \text { Council Bluffs, LA } & 46,844 & \text { Mauldin, SC } & 57,480 \\
\hline \text { Lenexa, KS } & 76,505 & \text { Rapid City, SD } & 47,788 \\
\hline \text { Georgetown, } \mathrm{KY} & 58,709 & \text { Franklin, TN } & 82,334 \\
\hline \text { Bossier City, LA } & 47,051 & \text { Allen, TX } & 104,524 \\
\hline \text { South Portland, ME } & 56,472 & \text { Orem, UT } & 54,515 \\
\hline \text { Rockville, MD } & 100,158 & \text { Colchester, VT } & 69,181 \\
\hline \text { Waltham, MA } & 75,106 & \text { Reston, VA } & 112,722 \\
\hline \text { Farmington Hills, MI } & 71,154 & \text { Mercer Island, WA } & 128,484 \\
\hline \text { Woodbury, MN } & 99,657 & \text { Morgantown, WV } & 38,060 \\
\hline \text { Olive Branch, MS } & 62,958 & \text { New Berlin, WI } & 74,983 \\
\hline \text { St. Peters, MO } & 57,728 & \text { Cheyenne, WY } & 56,593 \\
\hline
\end{array}
$$

a. Compute the mean and median for these houschold income data.
b. Compare the mean and median values for these data. What does this indicate about the distribution of household income data?
c. Compute the range and standard deviation for these household income data.
d. Compute the first and third quartiles for these household income data.
c. Are there any outliers in these data? What does this suggest about the data?

NCAA Basketball Game Scores. A sample of 10 NCAA college basketball game scores provided the following data.

$$
\begin{array}{lclcc}
\text { Winning Team } & \text { Points } & \text { Losing Team } & \text { Points } & \begin{array}{c}
\text { Winning } \\
\text { Margin }
\end{array} \\
\text { Arizona } & 90 & \text { Oregon } & 66 & 24 \\
\text { Duke } & 85 & \text { Georgetown } & 66 & 19 \\
\text { Florida State } & 75 & \text { Wake Forest } & 70 & 5 \\
\text { Kansas } & 78 & \text { Colorado } & 57 & 21 \\
\text { Kentucky } & 71 & \text { Notre Dame } & 63 & 8 \\
\text { Louisville } & 65 & \text { Tennessee } & 62 & 3 \\
\text { Oklahoma State } & 72 & \text { Texas } & 66 & 6 \\
\text { Purdue } & 76 & \text { Michigan State } & 70 & 6 \\
\text { Stanford } & 77 & \text { Southem Cal } & 67 & 10 \\
\text { Wisconsin } & 76 & \text { Illinois } & 56 & 20
\end{array}
$$

a. Compute the mean and standard deviation for the points scored by the winning teams.
b. Assume that the points scored by the winning teams for all NCAA games follow a bell-shaped distribution. Using the mean and standard deviation found in part (a), estimate the percentage of all NCAA games in which the winning team scores 84 or more points. Estimate the percentage of NCAA games in which the winning team scores more than 90 points.
c. Compute the mean and standard deviation for the winning margin. Do the data contain outliers? Explain.

Naples Half-Marathon Times. Naples, Florida, hosts a half-marathon (13.1-mile race) in January each year. The event attracts top runners from throughout the United States as well as from around the world. In the race results shown below 22 men and 31 women entered the 19-24 age class. Finish times in minutes are as follows. Times are shown in order of finish.

$$
\begin{array}{ccccccccc}
\text { Finish } & \text { Men } & \text { Women } & \text { Finish } & \text { Men } & \text { Women } & \text { Finish } & \text { Men } & \text { Women } \\
1 & 65.30 & 109.03 & 11 & 109.05 & 123.88 & 21 & 143.83 & 136.75 \\
2 & 66.27 & 111.22 & 12 & 110.23 & 125.78 & 22 & 148.70 & 138.20 \\
3 & 66.52 & 111.65 & 13 & 112.90 & 129.52 & 23 & & 139.00 \\
4 & 66.85 & 111.93 & 14 & 113.52 & 129.87 & 24 & & 147.18 \\
5 & 70.87 & 114.38 & 15 & 120.95 & 130.72 & 25 & & 147.35 \\
6 & 87.18 & 118.33 & 16 & 127.98 & 131.67 & 26 & & 147.50 \\
7 & 96.45 & 121.25 & 17 & 128.40 & 132.03 & 27 & 147.75 \\
8 & 98.52 & 122.08 & 18 & 130.90 & 133.20 & 28 & 153.88 \\
9 & 100.52 & 122.48 & 19 & 131.80 & 133.50 & 29 & 154.83 \\
10 & 108.18 & 122.62 & 20 & 138.63 & 136.57 & 30 & 189.27 \\
& & & & & & 31 & 189.28
\end{array}
$$

a. George Towett of Marietta, Georgia, finished in first place for the men and Lauren Wald of Gainesville, Florida, finished in first place for the women. Compare the first-place finish times for men and women. If the 53 men and women runners had competed as one group, in what place would Lauren have finished?
b. What is the median time for men and women runners? Compare men and women runners based on their median times.
c. Provide a five-number summary for both the men and the women.
d. Are there outliers in either group?
e. Show the boxplots for the two groups. Did men or women have the most variation in finish times? Explain.

Pharmaceutical Company Sales. Annual sales, in millions of dollars, for 21 pharmaceutical companies follow.
$$
\begin{array}{rrrrrr}
8408 & 1374 & 1872 & 8879 & 2459 & 11413 \\
608 & 14138 & 6452 & 1850 & 2818 & 1356 \\
10498 & 7478 & 4019 & 4341 & 739 & 2127 \\
3653 & 5794 & 8305 & & &
\end{array}
$$

a. Provide a five-number summary.
b. Compute the lower and upper limits.
c. Do the data contain any outliers?
d. Johnson & Johnson's sales are the largest on the list at $$\$ 14,138$$ million. Suppose a data entry error (a transposition) had been made and the sales had been entered as $$\$ 41,138$$ million. Would the method of detecting outliers in part (c) identify this problem and allow for correction of the data entry error?
c. Show a boxplot.

Cell Phone Companies Customer Satisfaction. Consumer Reports provides overall customer satisfaction scores for AT\&T, Sprint, T-Mobile, and Verizon cell-phone services in major metropolitan areas throughout the United States. The rating for each service reflects the overall customer satisfaction considering a variety of factors such as cost, connectivity problems, dropped calls, static interference, and customer support. A satisfaction scale from 0 to 100 is used with 0 indicating completely dissatisfied and 100 indicating completely satisfied. Suppose that the ratings for the four cell-phone services in 20 metropolitan areas are as shown below.

$$
\begin{array}{lcccc}
\text { Metropolitan Area } & \text { AT\&T } & \text { Sprint } & \text { T-Mobile } & \text { Verizon } \\
\text { Atlanta } & 70 & 66 & 71 & 79 \\
\text { Boston } & 69 & 64 & 74 & 76 \\
\text { Chicago } & 71 & 65 & 70 & 77 \\
\text { Dallas } & 75 & 65 & 74 & 78 \\
\text { Denver } & 71 & 67 & 73 & 77 \\
\text { Dotroit } & 73 & 65 & 77 & 79 \\
\text { Jacksonville } & 73 & 64 & 75 & 81 \\
\text { Las Vegas } & 72 & 68 & 74 & 81 \\
\text { Los Angeles } & 66 & 65 & 68 & 78 \\
\text { Miami } & 68 & 69 & 73 & 80 \\
\text { Minneapolis } & 68 & 66 & 75 & 77 \\
\text { Philadelphia } & 72 & 66 & 71 & 78 \\
\text { Phoenix } & 68 & 66 & 76 & 81 \\
\text { San Antonio } & 75 & 65 & 75 & 80 \\
\text { San Diego } & 69 & 68 & 72 & 79 \\
\text { San Francisco } & 66 & 69 & 73 & 75 \\
\text { Seattlo } & 68 & 67 & 74 & 77 \\
\text { St. Louis } & 74 & 66 & 74 & 79 \\
\text { Tampa } & 73 & 63 & 73 & 79 \\
\text { Washington } & 72 & 68 & 71 & 76
\end{array}
$$

a. Consider T-Mobile first. What is the median rating?
b. Develop a five-number summary for the T-Mobile service.
c. Are there outliers for T-Mobile? Explain.
d. Repeat parts (b) and (c) for the other three cell-phone services.
e. Show the boxplots for the four cell-phone services on one graph. Discuss what a comparison of the boxplots tells about the four services. Which service does Consumer Reports recommend as being best in terms of overall customer satisfaction?

Driving Speed and Fuel Efficiency. A department of transportation's study on driving speed and miles per gallon for midsize automobiles resulted in the following data:
$$
\begin{array}{l|llllllllll}
\text { Speed (Miles per Hour) } & 30 & 50 & 40 & 55 & 30 & 25 & 60 & 25 & 50 & 55 \\
\hline \text { Miles per Gallon } & 28 & 25 & 25 & 23 & 30 & 32 & 21 & 35 & 26 & 25
\end{array}
$$

Compute and interpret the sample correlation coefficient.

Physician Office Waiting Times. The average waiting time for a patient at an El Paso physician's office is just over 29 minutes, well above the national average of 21 minutes. In order to address the issue of long patient wait times, some physician's offices are using wait tracking systems to notify patients of expected wait times. Patients can adjust their arrival times based on this information and spend less time in waiting rooms. The following data show wait times (minutes) for a sample of patients at offices that do not have an office tracking system and wait times for a sample of patients at offices with an office tracking system.

$$
\begin{array}{cc}
\begin{array}{lc}
\text { Without Wait } \\
\text { Tracking System }
\end{array} & \begin{array}{l}
\text { With Wait } \\
\text { Tracking System }
\end{array} \\
24 & 31 \\
67 & 11 \\
17 & 14 \\
20 & 18 \\
31 & 12 \\
44 & 37 \\
12 & 9 \\
23 & 13 \\
16 & 12 \\
37 & 15
\end{array}
$$
a. What are the mean and median patient wait times for offices with a wait tracking system? What are the mean and median patient wait times for offices without a wait tracking system?
b. What are the variance and standard deviation of patient wait times for offices with a wait tracking system? What are the variance and standard deviation of patient wait times for visits to offices without a wait tracking system?
c. Do offices with a wait tracking system have shorter patient wait times than offices without a wait tracking system? Explain.
d. Considering only offices without a wait tracking system, what is the z-score for the tenth patient in the sample?
e. Considering only offices with a wait tracking system, what is the $z$-score for the sixth patient in the sample? How does this $z$-score compare with the $z$-score you calculated for part (d)?
f. Based on $z$-scores, do the data for offices without a wait tracking system contain any outliers? Based on $z$-scores, do the data for offices with a wait tracking system contain any outliers?

Smartphone Use. Smartphones have become ubiquitous for most people and have become the predominant means of communication among people. Consider the following data indicating the number of minutes in a month spent interacting with others via a smartphone for a sample of 50 smartphone users.
$$
\begin{array}{lllll}
353 & 458 & 404 & 394 & 416 \\
437 & 430 & 369 & 448 & 430 \\
431 & 469 & 446 & 387 & 445 \\
354 & 468 & 422 & 402 & 360 \\
444 & 424 & 441 & 357 & 435 \\
461 & 407 & 470 & 413 & 351 \\
464 & 374 & 417 & 460 & 352 \\
445 & 387 & 468 & 368 & 430 \\
384 & 367 & 436 & 390 & 464 \\
405 & 372 & 401 & 388 & 367
\end{array}
$$

a. What is the mean number of minutes spent interacting with others for this sample? How does it compare to the mean reported in the study?
b. What is the standard deviation for this sample?
c. Are there any outliers in this sample?

Best Hotels. Travel + Leisure magazine provides an annual list of the 500 best hotels in the world. The magazine provides a rating for each hotel along with a brief description that includes the size of the hotel, amenities, and the cost per night for a double room. A sample of 12 of the top-rated hotels in the United States follows.

$$
\begin{array}{llcc}
\text { Hotel } & \text { Location } & \text { Rooms } & \text { Cost/Night } \\
\text { Boulders Resort \& Spa } & \text { Phoenix, AZ } & 220 & 499 \\
\text { Disney's Wilderness Lodge } & \text { Orlando, FL } & 727 & 340 \\
\text { Four Seasons Hotel Beverly Hills } & \text { Los Angeles, CA } & 285 & 585 \\
\text { Four Seasons Hotel } & \text { Boston, MA } & 273 & 495 \\
\text { Hay-Adams } & \text { Washington, DC } & 145 & 495 \\
\text { Inn on Biltmore Estate } & \text { Asheville, NC } & 213 & 279 \\
\text { Loews Ventana Canyon Resort } & \text { Phoenix, AZ } & 398 & 279 \\
\text { Mauna Lani Bay Hotel } & \text { Island of Hawail } & 343 & 455 \\
\text { Montage Laguna Beach } & \text { Laguna Beach, CA } & 250 & 595 \\
\text { Sofitel Water Tower } & \text { Chicago, IL } & 414 & 367 \\
\text { St. Regis Monarch Beach } & \text { Dana Point, CA } & 400 & 675 \\
\text { The Broadmoor } & \text { Colorado Springs, CO } & 700 & 420
\end{array}
$$

a. What is the mean number of rooms?
b. What is the mean cost per night for a double room?
c. Develop a scatter diagram with the number of rooms on the horizontal axis and the cost per night on the vertical axis. Does there appear to be a relationship between the number of rooms and the cost per night? Discuss.
d. What is the sample correlation coefficient? What does it tell you about the relationship between the number of rooms and the cost per night for a double room? Does this appear reasonable? Discuss.

NFL Teams Worth. In 2014, the 32 teams in the National Football League (NFL) were worth, on average, $\$ 1.17$ billion, $5 \%$ more than in 2013 . The following data show the annual revenue ( $\$$ millions) and the estimated team value ( $\$$ millions) for the 32 NFL teams in 2014 (Forbes website).

a. Develop a scatter diagram with Revenue on the horizontal axis and Value on the vertical axis. Does there appear that there is any relationship between the two variables?
b. What is the sample correlation coefficient? What can you say about the strength of the relationship between Revenue and Value?

MLB Team Winning Percentages. Does a major league baseball team's record during spring training indicate how the team will play during the regular season? Over a six-year period, the correlation coefficient between a team's winning percentage in spring training and its winning percentage in the regular season is . 18 . Shown are the winning percentages for the 14 American League teams during a previous season.

a. What is the correlation coefficient between the spring training and the regular season winning percentages?
b. What is your conclusion about a team's record during spring training indicating how the team will play during the regular season? What are some of the reasons why this occurs? Discuss.

Automobile Speeds. Automobiles traveling on a road with a posted speed limit of 55 miles per hour are checked for speed by a state police radar system. Following is a frequency distribution of speed.

a. What is the mean speed of the automobiles traveling on this road?
b. Compute the variance and the standard deviation.

Annual Returns for Panama Railroad Company Stock. The Panama Railroad Company was established in 1850 to construct a railroad across the isthmus that would allow fast and easy access between the Atlantic and Pacific Oceans. The following table provides annual returns for Panama Railroad stock from 1853 through 1880.

a. Create a graph of the annual returns on the stock. The New York Stock Exchange eamed an annual average return of $8.4 \%$ from 1853 through 1880. Can you tell from the graph if the Panama Railroad Company stock outperformed the New York Stock Exchange?
b. Calculate the mean annual return on Panama Railroad Company stock from 1853 through 1880. Did the stock outperform the New York Stock Exchange over the same period?