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Compute the sample variance

Assignment Help Applied Statistics
Reference no: EM13728963

Question 1:

a. What is the average miles per gallon for city driving?

b. On average, how much higher is the miles per gallon for highway driving as compared to city driving?

FUEL ECONOMY INFORMATION FOR 10 AUTOMOBILES

City Highway

Car                                      Size                     Cylinders           MPG           MPG              Fuel

Audi A8

Large

12

13

19

Premium

BMW 328Xi

Compact

6

17

25

Premium

Cadillac CTS

Midsize

6

16

25

Regular

Chrysler 300

Large

8

13

18

Premium

Ford Focus

Compact

4

24

33

Regular

Hyundai Elantra

Midsize

4

25

33

Regular

Jeep Grand Cherokee

Midsize

6

17

26

Diesel

Pontiac G6

Compact

6

15

22

Regular

Toyota Camty

Midsize

4

21

31

Regular

Volkswagen Jetta

Compact

5

21

29

Regular

Question 2:

Business Week North American subscriber study collected data from a sample of 2861 subscribers. Fifty-nine percent of the respondents indicated an annual income of $75,000 or more, and 50% reported having an American Express credit card.

a. What is the population of interest in this study?

b. Is annual income a categorical or quantitative variable?

c. Is ownership of an American Express card a categorical or quantitative variable?

d. Does this study involve cross-sectional or time series data?

e. Describe any statistical inferences Business Week might make on the basis of the survey.

Question 3:

The following crosstabulation shows household income by educational level of the head of household (Statistical Abstract of the United States: 2008).

Educational Level

Under
25

Household Income ($1000s)

25.0-           50.0-       75.0-

49.9                74.9            99.9

100 or
more

Total

Not H.S. graduate

4207

3459

1389

539

367

9961

H.S. graduate

4917

6850

5027

2637

2668

22099

Some college

2807

5258

4678

3250

4074

20067

Bachelor's degree

885

2094

2848

2581

5379

13787

Beyond bach. deg.

290

829

1274

1241

4188

7822

Total

13106

18490

15216

10248

16676

73736

a. Compute the row percentages and identify the percent frequency distributions of income for households in which the head is a high school graduate and in which the head holds a bachelor's degree.

b. What percentage of households headed by high school graduates earn $75,000 or more? What percentage of households headed by bachelor's degree recipients earn $75,000 or more?

c. Construct percent frequency histograms of income for households headed by persons with a high school degree and for those headed by persons with a bachelor's degree. Is any relationship evident between household income and educational level?

Question 4:

Contains a portion of the data in the file named Fortune. Data on stockholders' equity, market value, and profits for a sample of 50 Fortune 500 companies are shown.

a. Prepare a crosstabulation for the variables Stockholders' Equity and Profit. Use classes of 0 -200, 200-400, . , 1000-1200 for Profit, and classes of 0-1200, 1200-2400,

4800-6000 for Stockholders' Equity.

b. Compute the row percentages for your crosstabulation in part (a).

c. What relationship, if any, do you notice between Profit and Stockholders' Equity?

Question 5:

The Los Angeles Times regularly reports the air quality index for various areas of South-em California. A sample of air quality index values for Pomona provided the following data: 28, 42, 58, 48, 45, 55, 60, 49, and 50.

a. Compute the range and interquartile range.

b. Compute the sample variance and sample standard deviation.

c. A sample of air quality index readings for Anaheim provided a sample mean of 48.5, a sample variance of 136, and a sample standard deviation of 11.66.

What compari¬sons can you make between the air quality in Pomona and that in Anaheim on the basis of these descriptive statistics?

Question 6:

Five observations taken for two variables follow.

x.

4

6

11

3

16

yi

50

50

40

60

30

a. Develop a scatter diagram with x on the horizontal axis.
b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
c. Compute and interpret the sample covariance.
d. Compute and interpret the sample correlation coefficient.

Question 7:

Consider the sample data in the following frequency distribution.

Class

Midpoint

Frequency

3-7

5

4

8-12

10

7

13-17

15

9

18-22

20

5

a. Compute the sample mean.

b. Compute the sample variance and sample standard deviation.

Reference no: EM13728963

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