Stats project | Statistics homework help

  

This project is made up of 4 different parts. The dataset for all 4 parts is given in the table below. Students are encouraged to use software (Minitab, excel etc.) to complete the project. For more help see your professor.

CARS: A sample of 20 cars, including measurements of fuel consumption (city mi/gal and highway mi/gal), weight (pounds), number of cylinders, engine displacement (in liters), amount of greenhouse gases emitted (in tons/year), and amount of tailpipe emissions of NOx (in lb/yr).

  

CAR

CITY

HWY

WEIGHT

CYLINDERS

DISPLACEMENT

MAN/AUTO

GHG

NOX

 

Chev.   Camaro

19

30

3545

6

3.8

M

12

34.4

 

Chev.   Cavalier

23

31

2795

4

2.2

A

10

25.1

 

Dodge   Neon

23

32

2600

4

2

A

10

25.1

 

Ford   Taurus

19

27

3515

6

3

A

12

25.1

 

Honda   Accord

23

30

3245

4

2.3

A

11

25.1

 

Lincoln   Cont.

17

24

3930

8

4.6

A

14

25.1

 

Mercury   Mystique

20

29

3115

6

2.5

A

12

34.4

 

Mitsubishi   Eclipse

22

33

3235

4

2

M

10

25.1

 

Olds.   Aurora

17

26

3995

8

4

A

13

34.4

 

Pontiac   Grand Am

22

30

3115

4

2.4

A

11

25.1

 

Toyota   Camry

23

32

3240

4

2.2

M

10

25.1

 

Cadillac   DeVille

17

26

4020

8

4.6

A

13

34.4

 

Chev.   Corvette

18

28

3220

8

5.7

M

12

34.4

 

Chrysler   Sebring

19

27

3175

6

2.5

A

12

25.1

 

Ford   Mustang

20

29

3450

6

3.8

M

12

34.4

 

BMW   3-Series

19

27

3225

6

2.8

A

12

34.4

 

Ford   Crown Victoria

17

24

3985

8

4.6

A

14

25.1

 

Honda   Civic

32

37

2440

4

1.6

M

8

25.1

 

Mazda   Protege

29

34

2500

4

1.6

A

9

25.1

 

Hyundai   Accent

28

37

2290

4

1.5

A

9

34.4

Part I

Generally the first step to analyze a dataset that is given to you is to identify the type of data, and picture the data using graphs etc. Use the data set above to answer the following questions:

1. Assume that the car column represents all car models. Use the random number Table B, to generate a simple random sample of 15 car models from the set above.

2. Classify all the columns: car, city, HWY, weight, cylinders, displacement man/auto GHG NOX according to the following:

i. Categorical or quantitative

ii. Discrete or continuous or none

iii. Levels of measurement: nominal, ordinal, interval or ratio.

3. Make a frequency distribution for MAN/AUTO

4. Make a frequency distribution for DISPLACEMENT. (also include the column for cumulative frequency)

5. Make a bar graph or pie chart for MAN/AUTO.

6. Make a histogram for DISPLACEMENT.

i. Determine the type of skewness- left, right, symmetric or none.

ii. Determine the variability-high or low.

7. Make a stemplot for CITY

i. Determine the type of skewness- left, right, symmetric or none.

ii. Determine the variability-high or low or none.

8. Make a dotplot for CYLINDER.

i. Determine the type of skewness- left, right , symmetric or none.

ii. Determine the variability-high or low, or none.

Part II

To summarize a dataset sometimes we have to find the measures of center or variation. Sometime we have to compute quartiles and make boxplots. Summarize the datasets given in the table above by answering the following questions:

1. Find the measures of center for the column NOX (i.e. the mean, mode, median, midrange).

2. Use the measures of center (mean, median, mode) to determine the type of skewness (to the right, to the left, or symmetric) in NOX.

3. Calculate the measures of variation for the datset-GHG, that is, find the standard deviation, the variance and interquartile range.

i. What does the standard deviation measure for this dataset?

ii. What does the interquartile range measure for this dataset?

4.  Use the HWY data above to answer the following:

i. Make a 5 number summary

ii.  Make a boxplot.

iii. Identify any outliers.

Part III

To determine whether there is any linear relationship between the number of cylinders (CYLINDERS) a car has and the greenhouse emission gasses (GHG) , first we make a scatterplot for the data, then we calculate the linear correlation coefficient. If there is strong linear correlation then we do regression. Answer the following questions:

1. Make a scatterplot for CYLINDERS and GHG. Use your independent variable as CYLINDERS and dependent variable as GHG.

i. Describe the type of linear correlation- positive, negative, no correlation. Is it nonlinear?

2. Find the linear correlation coefficient between CLYLINERS and GHG. 

i. Describe the linear correlation coefficient. Is it positive or negative? Is it strong, moderate or week? 

ii. Use Table A6 and to determine whether there is correlation between CYLINDER and GHG in the population.

3. Find the regression line between CYLINDERS and GHG.

i. What is the meaning of the slope for your regression equation?

ii. What is the meaning of y-intercept for your regression equation?

iii. Estimate the greenhouse emission gasses amount if the number of cylinders for cars could be 5. 

Part IV

The ultimate goal in any statistical study is to make inferences about the population using the sample information. This is called inferential statistics.

1. Suppose we are interested to predict the average tailpipe emissions of NOx (in lb/yr)(NOX) per year for all car models using the sample that is given in the column NOX. One way to do this is to construct a confidence interval for the population mean tailpipe emission of NOX. 

i. Construct a 99% confidence interval for the mean tailpipe emission of NOX. Assume that the population of the tailpipe emission of NOX values are normally distributed. Find your point estimate, determine the sampling distribution, find the critical value, find the margin of error, and find the confidence interval.

ii. Conclude the confidence interval.

2. Suppose we are interested to test hypotheses to determine a value for the population mean engine displacement (in liters) for all car models. 

i. Use a 0.01 significance level to investigate whether the mean engine displacement is more than 2.5 liters. Assume that the engine displacement of all cars is normally distributed. Set hypotheses, find your point estimate, determine the sampling distribution, find the test statistics, find the p-value and 

ii. Conclude the test.

3. Suppose we are also interested in the proportion of car models that have 4 cylinders in a sample. Suppose it is known than about 50% of all car models have 4 cylinders. Use the dataset CYLINDERS as a sample, and find the probability of randomly selecting a sample of 20 car models that contains more 4 cylinder cars than the number of 4 cylinder cars in dataset CYLINDERS. Find the sample proportion, determine the sampling distribution (normal), and find the probability (See chapter 15-the last couple of slides). 

4. Is there evidence that automatic cars are more common than manual cars? 

i. Use a 0.05 significance level to conduct a suitable hypotheses test using the dataset MAN/AUTO as a sample to conduct your test. Set hypotheses, find your point estimate, determine the sampling distribution, find the test statistic, find the p-value and 

ii. conclude the test.

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