# GM 533 Statistics Final Examination.

Data Set Ford Mustang Automobiles

PRICE CONVERT AGE MILES TRANS Variables:

12688 0 1 8200 0 PRICE = Asking price in dollars

11500 0 1 27000 1 CONVERT = 1 if convertible and 0 if not

11650 0 1 3000 0 AGE = age of car in years

10995 1 2 27000 1 MILES = odometer reading in miles

6200 0 3 55000 1 TRANS = 1 if automatic and 0 if manual

9500 0 3 22000 0

8700 0 3 25000 1 Source: Practical Data Analysis 2nd, Vol I, II

12500 0 2 23800 0 Bryant-Smith McGraw-Hill ISBN -13:978-0-69-778527-5

10488 1 4 20000 0 For Applied Managerial Statistics GM533 DeVry University

5988 0 4 37000 0

7288 1 5 84000 1

3590 0 5 55000 0

2800 0 6 62000 0

6995 1 7 78000 1

4900 0 7 60000 0

2488 0 7 67000 1

4200 1 8 65000 1

12990 1 1 13300 1

14500 1 3 31000 1

10900 1 3 4000 1

13500 1 3 23000 0

12000 0 3 89000 0

8500 0 3 34000 1

4388 0 4 80000 0

3000 0 7 95000 0

3900 0 8 90000 0

3350 0 8 91000 0

10500 0 3 17000 0

12988 0 1 21000 1

6500 0 3 73000 0

12900 1 2 19000 0

9000 0 2 32000 0

7000 0 6 56000 0

5900 0 4 110000 1

2500 0 6 92000 0

1) Use descriptive statistics to describe the price of the autos in the data set TCO A

assuming it is a sample. 5 points

2) Draw a histogram of the Price of autos in the data set. TCO A

5 points

3) Compare the average price of the five autos with the lowest mileage TCO A

to the average price of the five autos with the highest mileage. 5 points

Use a column graph to illustrate your findings.

4) Stanford-Binet IQ Test scores are normally distributed with a mean score of 100 TCO B

and a standard deviation of 16.

25 points

a) Find the probability that a randomly selected person has an IQ score over 133

b) Find the probability that a randomly selected person has an IQ score under 86

c) Find the probability that a randomly selected person has an IQ score between 72 and 128

d) Find the probability a randomly selected person has an IQ within 1.5 standard deviations of the mean.

e) Find the lowest IQ score for a person in the upper 6% of the Stanford-Binet IQ Test score distribution.

Use the following Data Set A to answer questions 5, 6, and 7.

Data Set A

5

8

12

3

14

2

4

7

5) What is the mean of the data in set A?

a) 1.52 5 points TCO A

b) 6

c) 6.87

d) 55

6) What is the range of the data in Data Set A? 5 points TCO A

a) The distance to the target

b) The difference of the maximum and minimum observations

c) The average squared deviation from the mean

d) kurtosis divided by skewness

7) Why can’t the Mode be calculated for Data Set A? 5 points TCO A

a) No observation occurs more than once

b) The Mean is greater than the Median

c) The number of observations is not 30 or more

d) EXCEL doesn’t work on small data sets.

8) Which graph best shows the relationship between the Year and the Price Index (CPI)? TCO A

Choose the best answer a), b), c), d) 5 points

9) Which of the following is a probability distribution? 5 points TCO B

a) b)

X P(X) X P(X)

Green 0.5 5 0.1

Red 0.3 12.5 0.5

Blue 0.1 26.2 0.4

c) d)

X P(X) X P(X)

Sam 0.2 0.4 0.1

Ned 0.5 0.4 0.5

Sally 0.4 0.2 0.3

10) Tires made by the Schlock Company have mean life of 50,000 miles, Standard Deviation

of 4,200 miles. What mileage should the company guarantee so that no more

than 3% fail to make the guaranteed mileage if the distribution is normal? 10 points

Data Set Ford Mustang Automobiles

PRICE CONVERT AGE MILES TRANS Variables:

12688 0 1 8200 0 PRICE = Asking price in dollars

11500 0 1 27000 1 CONVERT = 1 if convertible and 0 if not

11650 0 1 3000 0 AGE = age of car in years

10995 1 2 27000 1 MILES = odometer reading in miles

6200 0 3 55000 1 TRANS = 1 if automatic and 0 if manual

9500 0 3 22000 0

8700 0 3 25000 1 Source: Practical Data Analysis 2nd, Vol I, II

12500 0 2 23800 0 Bryant-Smith McGraw-Hill ISBN -13:978-0-69-778527-5

10488 1 4 20000 0 For Applied Managerial Statistics GM533 DeVry University

5988 0 4 37000 0

7288 1 5 84000 1

3590 0 5 55000 0

2800 0 6 62000 0

6995 1 7 78000 1

4900 0 7 60000 0

2488 0 7 67000 1

4200 1 8 65000 1

12990 1 1 13300 1

14500 1 3 31000 1

10900 1 3 4000 1

13500 1 3 23000 0

12000 0 3 89000 0

8500 0 3 34000 1

4388 0 4 80000 0

3000 0 7 95000 0

3900 0 8 90000 0

3350 0 8 91000 0

10500 0 3 17000 0

12988 0 1 21000 1

6500 0 3 73000 0

12900 1 2 19000 0

9000 0 2 32000 0

7000 0 6 56000 0

5900 0 4 110000 1

2500 0 6 92000 0

11) Using the "Ford Mustang Data Set" to represent a random sample, determine a 95% TCO C

confidence interval for the mean price of Ford Mustangs. 10 points

12) Using the "Ford Mustang Data Set" to represent a random sample, determine a 90% TCO C

confidence interval for the mean value of odometer mileage.(MILES) 10 points

13) The Internal Revenue Service has stated that historically 85% of federal tax returns TCO B

filed are free of arithmetic errors. A random sample of 25 returns is selected and

checked carefully for arithmetic errors. Assuming independence, find the probability that:

hint: Binomial problem 20 points

a. all 25 returns are free of arithmetic errors.

b. at most 23 returns are free of arithmetic errors.

c. more than 17 are free of arithmetic errors.

14) A new brand of laptop battery is produced by ZELCON. The company claims that the TCO B

battery will last for an extended period of time before a recharge is necessary. A sample

of 49 batteries is tested for the length of usage time to recharge. The sample results are

as follows: 20 points

Sample Size = 49

Sample Mean = 6.4 hrs.

Sample Standard Deviation = 1.3 hrs.

a. Construct a 95% confidence interval for the average length of usage time to recharge. TCO C

b. Interpret this interval.

c. How large a sample size will need to be selected if we wish to have a 95% confidence

interval with a margin for error of .25 hours?

16. Bill Smith is the Worthington Township manager. When citizens request a traffic light, the

staff assesses the traffic flow at the requested intersection. Township policy requires the installation of

a traffic light when an intersection averages more than 150 vehicles per hour. A random sample of 50

vehicle counts is done. The results are as follows: 40 points

Sample Size = 50

Sample Mean = 159.3 vehicles/hr.

Sample Standard Deviation = 27.5 vehicles/hr.

Does the sample data provide evidence to conclude that the installation of the traffic light is warranted

(using α= .10)? Use the hypothesis testing procedure outlined below.

a. Formulate the null and alternative hypotheses. TCO D

b. State the level of significance.

c. Find the critical value (or values), and clearly show the rejection and nonrejection regions.

d. Compute the test statistic.

e. Decide whether you can reject Ho and accept Ha or not.

f. Explain and interpret your conclusion in part e. What does this mean?

g. Find the observed p-value for the hypothesis test and interpret this value. What does this mean?

h. Does this sample data provide evidence (with α = 0.10), that the installation of the traffic light

is warranted?

17) Given the following regression output:

SUMMARY OUTPUT 15 points

Regression Statistics TCO E

Multiple R 0.835

R Square 0.697

Adjusted R Square 0.674

Standard Error 0.972

Observations 15

ANOVA

df SS MS F Significance F

Regression 1 28.287 28.287 29.970 0.000

Residual 13 12.270 0.944

Total 14 40.557

Standard Lower Upper

Coefficients Error t Stat P-value 95% 95%

Intercept -0.309 3.109 -0.099 0.922 -7.025 6.407

X 0.212 0.039 5.475 0.000 0.128 0.296

A) Approximately what percentage of the variation in the Y variable

is explained by the regression?

PRICE CONVERT AGE MILES TRANS Variables:

12688 0 1 8200 0 PRICE = Asking price in dollars

11500 0 1 27000 1 CONVERT = 1 if convertible and 0 if not

11650 0 1 3000 0 AGE = age of car in years

10995 1 2 27000 1 MILES = odometer reading in miles

6200 0 3 55000 1 TRANS = 1 if automatic and 0 if manual

9500 0 3 22000 0

8700 0 3 25000 1 Source: Practical Data Analysis 2nd, Vol I, II

12500 0 2 23800 0 Bryant-Smith McGraw-Hill ISBN -13:978-0-69-778527-5

10488 1 4 20000 0 For Applied Managerial Statistics GM533 DeVry University

5988 0 4 37000 0

7288 1 5 84000 1

3590 0 5 55000 0

2800 0 6 62000 0

6995 1 7 78000 1

4900 0 7 60000 0

2488 0 7 67000 1

4200 1 8 65000 1

12990 1 1 13300 1

14500 1 3 31000 1

10900 1 3 4000 1

13500 1 3 23000 0

12000 0 3 89000 0

8500 0 3 34000 1

4388 0 4 80000 0

3000 0 7 95000 0

3900 0 8 90000 0

3350 0 8 91000 0

10500 0 3 17000 0

12988 0 1 21000 1

6500 0 3 73000 0

12900 1 2 19000 0

9000 0 2 32000 0

7000 0 6 56000 0

5900 0 4 110000 1

2500 0 6 92000 0

1) Use descriptive statistics to describe the price of the autos in the data set TCO A

assuming it is a sample. 5 points

2) Draw a histogram of the Price of autos in the data set. TCO A

5 points

3) Compare the average price of the five autos with the lowest mileage TCO A

to the average price of the five autos with the highest mileage. 5 points

Use a column graph to illustrate your findings.

4) Stanford-Binet IQ Test scores are normally distributed with a mean score of 100 TCO B

and a standard deviation of 16.

25 points

a) Find the probability that a randomly selected person has an IQ score over 133

b) Find the probability that a randomly selected person has an IQ score under 86

c) Find the probability that a randomly selected person has an IQ score between 72 and 128

d) Find the probability a randomly selected person has an IQ within 1.5 standard deviations of the mean.

e) Find the lowest IQ score for a person in the upper 6% of the Stanford-Binet IQ Test score distribution.

Use the following Data Set A to answer questions 5, 6, and 7.

Data Set A

5

8

12

3

14

2

4

7

5) What is the mean of the data in set A?

a) 1.52 5 points TCO A

b) 6

c) 6.87

d) 55

6) What is the range of the data in Data Set A? 5 points TCO A

a) The distance to the target

b) The difference of the maximum and minimum observations

c) The average squared deviation from the mean

d) kurtosis divided by skewness

7) Why can’t the Mode be calculated for Data Set A? 5 points TCO A

a) No observation occurs more than once

b) The Mean is greater than the Median

c) The number of observations is not 30 or more

d) EXCEL doesn’t work on small data sets.

8) Which graph best shows the relationship between the Year and the Price Index (CPI)? TCO A

Choose the best answer a), b), c), d) 5 points

9) Which of the following is a probability distribution? 5 points TCO B

a) b)

X P(X) X P(X)

Green 0.5 5 0.1

Red 0.3 12.5 0.5

Blue 0.1 26.2 0.4

c) d)

X P(X) X P(X)

Sam 0.2 0.4 0.1

Ned 0.5 0.4 0.5

Sally 0.4 0.2 0.3

10) Tires made by the Schlock Company have mean life of 50,000 miles, Standard Deviation

of 4,200 miles. What mileage should the company guarantee so that no more

than 3% fail to make the guaranteed mileage if the distribution is normal? 10 points

Data Set Ford Mustang Automobiles

PRICE CONVERT AGE MILES TRANS Variables:

12688 0 1 8200 0 PRICE = Asking price in dollars

11500 0 1 27000 1 CONVERT = 1 if convertible and 0 if not

11650 0 1 3000 0 AGE = age of car in years

10995 1 2 27000 1 MILES = odometer reading in miles

6200 0 3 55000 1 TRANS = 1 if automatic and 0 if manual

9500 0 3 22000 0

8700 0 3 25000 1 Source: Practical Data Analysis 2nd, Vol I, II

12500 0 2 23800 0 Bryant-Smith McGraw-Hill ISBN -13:978-0-69-778527-5

10488 1 4 20000 0 For Applied Managerial Statistics GM533 DeVry University

5988 0 4 37000 0

7288 1 5 84000 1

3590 0 5 55000 0

2800 0 6 62000 0

6995 1 7 78000 1

4900 0 7 60000 0

2488 0 7 67000 1

4200 1 8 65000 1

12990 1 1 13300 1

14500 1 3 31000 1

10900 1 3 4000 1

13500 1 3 23000 0

12000 0 3 89000 0

8500 0 3 34000 1

4388 0 4 80000 0

3000 0 7 95000 0

3900 0 8 90000 0

3350 0 8 91000 0

10500 0 3 17000 0

12988 0 1 21000 1

6500 0 3 73000 0

12900 1 2 19000 0

9000 0 2 32000 0

7000 0 6 56000 0

5900 0 4 110000 1

2500 0 6 92000 0

11) Using the "Ford Mustang Data Set" to represent a random sample, determine a 95% TCO C

confidence interval for the mean price of Ford Mustangs. 10 points

12) Using the "Ford Mustang Data Set" to represent a random sample, determine a 90% TCO C

confidence interval for the mean value of odometer mileage.(MILES) 10 points

13) The Internal Revenue Service has stated that historically 85% of federal tax returns TCO B

filed are free of arithmetic errors. A random sample of 25 returns is selected and

checked carefully for arithmetic errors. Assuming independence, find the probability that:

hint: Binomial problem 20 points

a. all 25 returns are free of arithmetic errors.

b. at most 23 returns are free of arithmetic errors.

c. more than 17 are free of arithmetic errors.

14) A new brand of laptop battery is produced by ZELCON. The company claims that the TCO B

battery will last for an extended period of time before a recharge is necessary. A sample

of 49 batteries is tested for the length of usage time to recharge. The sample results are

as follows: 20 points

Sample Size = 49

Sample Mean = 6.4 hrs.

Sample Standard Deviation = 1.3 hrs.

a. Construct a 95% confidence interval for the average length of usage time to recharge. TCO C

b. Interpret this interval.

c. How large a sample size will need to be selected if we wish to have a 95% confidence

interval with a margin for error of .25 hours?

16. Bill Smith is the Worthington Township manager. When citizens request a traffic light, the

staff assesses the traffic flow at the requested intersection. Township policy requires the installation of

a traffic light when an intersection averages more than 150 vehicles per hour. A random sample of 50

vehicle counts is done. The results are as follows: 40 points

Sample Size = 50

Sample Mean = 159.3 vehicles/hr.

Sample Standard Deviation = 27.5 vehicles/hr.

Does the sample data provide evidence to conclude that the installation of the traffic light is warranted

(using α= .10)? Use the hypothesis testing procedure outlined below.

a. Formulate the null and alternative hypotheses. TCO D

b. State the level of significance.

c. Find the critical value (or values), and clearly show the rejection and nonrejection regions.

d. Compute the test statistic.

e. Decide whether you can reject Ho and accept Ha or not.

f. Explain and interpret your conclusion in part e. What does this mean?

g. Find the observed p-value for the hypothesis test and interpret this value. What does this mean?

h. Does this sample data provide evidence (with α = 0.10), that the installation of the traffic light

is warranted?

17) Given the following regression output:

SUMMARY OUTPUT 15 points

Regression Statistics TCO E

Multiple R 0.835

R Square 0.697

Adjusted R Square 0.674

Standard Error 0.972

Observations 15

ANOVA

df SS MS F Significance F

Regression 1 28.287 28.287 29.970 0.000

Residual 13 12.270 0.944

Total 14 40.557

Standard Lower Upper

Coefficients Error t Stat P-value 95% 95%

Intercept -0.309 3.109 -0.099 0.922 -7.025 6.407

X 0.212 0.039 5.475 0.000 0.128 0.296

A) Approximately what percentage of the variation in the Y variable

is explained by the regression?

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