Statistics for Business and Economics chapter 02

Graduate, is the percent frequency distribution for households headed by high school graduates.. The fourth row, labeled Bachelor's Degree, is the percent frequency distribution for hous

No Opinion 16.7%

No 35.0%

010203040506070

CSI 36%

Trace 18%

Housewives 26%

b CBS and NBC are tied, each with 17 of the top rated television shows ABC is a close third with

15 The fact that the three networks are so close is surprising FOX, the newest television

network, does not have the history to compete with the other three networks in term of the top rated shows in television history

7

Williams 16%

Brown 14%

Davis 12%

Johnson 20%

Jones 14%

Smith 24%

Rating Frequency Relative Frequency

b Where do you live now?

What do you consider the ideal community?

c Most adults are now living in a city (32%)

d Most adults consider the ideal community a small town (30%)

e Percent changes by living area: City -8%, Suburb -1%, Small Town +4%, and Rural Area +5%.Suburb living is steady, but the trend would be that living in the city would decline while

living in small towns and rural areas would increase

e 40% + 10% = 50% of adults in Spain think the European Central Bank is doing a bad or terrible job in handling the credit problems Only 4% of adults in Spain think the European Central Bank

is doing a good or excellent job

Both countries show pessimism and relatively low confidence in how the banks are handling the credit problems in the financial markets But in comparing the two countries, adults in Spain show more concern and more pessimism about the bank’s ability compared to adults in the UnitedStates

less than or equal to 19 10 20

13

024681012141618

Class Frequency Percent Frequency

Salary Cumulative Percent Frequency

Less than or equal to 169 20

d

e There is skewness to the right

f (3/20)(100) = 15%

17 a The highest price stock is for IBM with a price of $109 per share

The lowest price stock is for Alcoa with a price of $11 per share

b A class size of 10 results in 10 classes

Price per Share Frequenc

The general shape of the distribution is skewed to the right Half of the companies (15) have a price per share less than $30 A mid-priced stock appears to be in the $30 to $49 range, while the most frequently priced stock is in the $20 to $29 range

Five stocks are less than $20 per share (Alcoa, Bank of America, General Electric, Intel and Pfizer)

Four stocks are $60 or more per share (3M, Chevron, ExxonMobil and IBM)

d A variety of comparisons are possible depending upon when the study is done

18 a The lowest holiday spending is $180; the highest $2050

d The holiday spending ranges from $0 to less than $2250 The majority of the spending is between

$250 and $1000 with 16 of the 25 customers, 64%, in this range The middle or average spending is around $750 per customer The distribution has a positive skewness with two consumers above $1750 One consumer is above $2000

0 5 10 15 20 25 30 35

Time

b Histogram of Off-Course Income

Note: The first class is labeled 5000 and provides the golfers who had an off-course income in

the range 0 to 4999 or less than 5000 These were the golfers with less than $5 million in

off-course income

c Off-course income is skewed to the right Only Tiger Woods earns over $50 million

d Considering the top 50 golfers, the majority (60%) earn less than $5 million in off-course income per year 60% + 18% = 78% earn less than $10 million Five golfers (10%) earn between $20 million and $30 million Tiger Woods with $99.8 million and Phil Mickelson with $40.2 million

in off-course income are clearly the leaders in this income category

21 a/b.

ComputerUsage (Hours) Frequency FrequencyRelative

3

50

20 40

2 ­ 15

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13 7

14 5  5

b Observations such as the following can be made using the stem-and-leaf display

 The daily rate varies from $75 to $145

 Typical mid-priced daily rates are $95 to $115 with the average daily rate around $100

 A daily rate in excess of $115 should be considered relatively high High daily rates of $137 and $145 were found at three ski resorts

b Most frequent age group: 40-44 with 9 runners

c 43 was the most frequent age with 5 runners

d 4/40 = 10% of the runners were something.” With only 10% of the registrants

“20-something,” the article pointed out that surprisingly few registrants were in this age group One suggested reason was that “20-somethings” don’t have the time to train for a 13.1 mile race For

“20-somethings,” college, starting careers, and starting families may take priority over training for long distance races

29 a

1

0.0 15.4 83.3

2 100.0 100.0 100.0 Total

0.0 16.7 83.3 100.0

Total

d Category A values for x are always associated with category 1 values for y.  Category B values for x are usually associated with category 1 values for y.  Category C values for x are usually associated  with category 2 values for y.

30 a

The second row, labeled H.S. Graduate, is the percent frequency distribution for households headed 

by high school graduates. The fourth row, labeled Bachelor's Degree, is the percent frequency distribution for households headed by bachelor's degree recipients

b The percentage of households headed by high school graduates earning $75,000 or more is 11.93% + 12.07 = 24.00%. The percent of households headed by bachelor's degree recipients earning 

$75,000 or more is 18.72% + 39.02% = 57.74%

c The percent frequency histogram for high school graduates. 

The histograms show that households headed by a college graduate with a bachelor’s degree earn more than households headed by a high school graduate. Yes, there is a positive relationship between education level and income. 

b The column percentages show that 25.11% of households earning $100,000 or more were headed 

by persons having schooling beyond a bachelor's degree. The row percentages show that 53.54% of the households headed by persons with schooling beyond a bachelor's degree earned $100,000 or more. These percentages are different because they came from different percent frequency 

distributions and provide different kinds of information

c Compare the "under 25" percent frequency distributions to the "Total" percent frequency 

distributions. We see that for this low income level the percentage with lower levels of education is higher than for the overall population and the percentage with higher levels of education is lower than for the overall population

Compare the "100 or more" percent frequency distribution to "Total" percent frequency distribution

We see that for this high income level the percentage with lower levels of education is lower than for the overall population and the percentage with higher levels of education is higher than for the overall population

From the comparisons it is clear that there is a positive relationship between household incomes andthe education level of the head of the household

b Among low handicap golfers, 1/10 = 10% of the women think the greens are too fast and 10/50 = 20% of the men think the greens are too fast. So, for the low handicappers, the men show a higher percentage who think the greens are too fast

c Among the higher handicap golfers, 39/51 = 43% of the woman think the greens are too fast and 25/50 = 50% of the men think the greens are too fast. So, for the higher handicap golfers, the men show a higher percentage who think the greens are too fast

d This is an example of Simpson's Paradox. At each handicap level a smaller percentage of the women think the greens are too fast. But, when the crosstabulations are aggregated, the result is reversed and we find a higher percentage of women who think the greens are too fast.

The hidden variable explaining the reversal is handicap level. Fewer people with low handicaps think the greens are too fast, and there are more men with low handicaps than women

5 Year Average Return

1.00-1.24 14 31.0

c Higher expense ratios are associated with Domestic Equity funds and lower expense ratios are

associated with Fixed Income fund

36 a The scatter diagram is shown below:

b There is some indication that higher 5-year returns are associated with higher net asset values

b Higher fuel efficiencies are associated with smaller displacement engines and lower fuel

efficiencies are associated with larger displacement engines

c The scatter diagram is shown below:

d The scatter diagram shows that lower fuel efficiencies are associated with larger displacement engines.

e It is easier to see the relationship between the two variables using the scatter diagram

c 34.4% select another major So 100% - 34.4% = 65.6% select one of the five most popular majors.

d Business Administration is the most popular major selected by incoming freshmen, 20.3%

40 a Frequency distribution and percent frequency distribution of sales by division.

c Chevrolet is General Motors leading division with 61% of the vehicles sold This is considered General Motors most important division.

d Based on the percentages shown, the Hummer division at 1% and Saab division at 1% would be good candidates for General Motors to consider discontinuing Chevrolet at 61% and GMC at 12% account for 73% of the total vehicles sold General Motors would be almost certain to maintain these two divisions

Pontiac remains a solid contributor with 9% of vehicles sold At the time it was doubtful than General Motors would be able to maintain all three of the other divisions Some elimination or merging of divisions was anticipated for Saturn 6%, Buick 5%, and Cadillac 5%

c The distribution is skewed to the right.

d Dividend yield ranges from 0% to over 9% The most frequent range is 3.0% to 3.9% Average dividend yields looks to be between 3% and 4% Over 50% of the companies (16) pay from 2.0 %

to 3.9% Five companies (AT&T, DuPont, General Electric, Merck, and Verizon) pay 5.0% or more Four companies (Bank of America, Cisco Systems, Hewlett-Packard, and J.P Morgan Chase) pay less than 1%

e General Electric had an unusually high dividend yield of 9.2% 500 shares at $14 per share is an investment of 500($14) = $7,000 A 9.2% dividend yield provides 092(7,000) = $644 of dividendincome per year

b The distribution if nearly symmetrical It could be approximated by a bell-shaped curve.

c 10 of 30 or 33% of the scores are between 1400 and 1599 The average SAT score looks to be a little over 1500 Scores below 800 or above 2200 are unusual

b Florida has had the most Super Bowl with 15, or 15/43(100) = 35% Florida and California have been the states with the most Super Bowls A total of 15 + 11 = 26, or 26/43(100) = 60% Only 3Super Bowls, or 3/43(100) = 7%, have been played in the cold weather states of Michigan and Minnesota.

c

d The most frequent winning points have been 0 to 4 points and 15 to 19 points Both occurred in

10 Super Bowls There were 10 close games with a margin of victory less than 5 points,

10/43(100) = 23% of the Super Bowls There have also be 10 games, 23%, with a margin of victory more than 20 points

e The closest games was the 25th Super Bowl with a 1 point margin It was played in Florida The largest margin of victory occurred one year earlier in the 24th Super Bowl It had a 45 point margin and was played in Louisiana More detailed information not available from the text information

25th Super Bowl: 1991 New York Giants 20 Buffalo Bills 19, Tampa Stadium, Tampa, FL

24th Super Bowl: 1990 San Francisco 49ers 55 Denver Broncos 10, Superdome, New Orleans, LA

Note: The data set SuperBowl contains a list of the teams and the final scores of the 43 Super Bowls This data set can be used in Chapter 2 and Chapter 3 to provide interesting data

summaries about the points scored by the winning team and the points scored by the losing team

in the Super Bowl For example, using the median scores, the median Super Bowl score was 28

c High positive skewness.

d 17 states (34%) have a population less than 2.5 million Over half of the states have population less than 5 million (29 states – 58%) Only eight states have a population greater than 10 million (California, Florida, Illinois, Michigan, New York, Ohio, Pennsylvania and Texas) The largest state is California (35.9 million) and the smallest state is Wyoming (500 thousand)

45 a

c The most frequent range for temperature was in the 60s (9 of 20) Only one low temperature was

above 54 High temperatures were mostly 41 to 68, while low temperatures were mostly 21 to 47

Low was 11; High was 84

d

High Temp Frequency Low Temp Frequency

48 a Level of Support Percent Frequency

Favor more than oppose 1871/5372 = 34.83

Oppose more than favor 1135/5372 = 21.13

The results show support for a higher tax Note that 30.10% + 34.83% = 64.93% of the

respondents said they strongly favor or favor more than oppose a higher tax on higher carbon emission cars

b Country Percent Frequency

c Converting the entries in the crosstabulation into column percentages provides the following results:

Country

Considering the percentage of respondents who favor the higher tax by either saying “strongly favor” or “favor more than oppose”, we have the following favorable support for the higher tax in each country

49 a The batting averages for the junior and senior years for each player are as follows:

b The combined or aggregated two-year crosstabulation is as follows:

Based on this crosstabulation, the batting average for each player is as follows:

Combined 2-Year Batting

Combined Junior/Senior Years

or before.  All of the buildings using propane are older

Observations from the row percentages crosstabulation

Most of the buildings in the CG&E service area use electricity or natural gas.  In the period 1973 or before most used natural gas.  From  1974­1986, it is fairly evenly divided between electricity and natural gas.  Since 1987 almost all new buildings are using electricity or natural gas with natural gasbeing the clear leader