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(Solved) MATH2209 Lab 6 No quiz for Lab 6. Please submit answers by


i have this statistics assignment to fee finish thanks . for you help


MATH2209 Lab 6

 

No quiz for Lab 6. Please submit answers by uploading a file to Moodle.

 

Question 1

 

Assume you are doing a test of significance for comparing counts in a two-way

 

contingency table. For the following cases that could arise, look up the P-value as

 

accurately as possible using the appropriate statistical table.

 


 

Cas

 

e

 


 

Numbe

 

r of

 

Rows

 


 

Number

 

of

 

Columns

 


 

Test

 

Statistic

 


 

1

 


 

2

 


 

2

 


 

X2 = 6.498

 


 

2

 


 

2

 


 

4

 


 

X2 = 6.498

 


 

3

 


 

4

 


 

2

 


 

X2 = 6.498

 


 

4

 


 

4

 


 

5

 


 

X2 = 6.498

 


 

5

 


 

6

 


 

8

 


 

X2 = 6.498

 


 

Degrees of

 

Freedom

 


 

Value(s) on

 

Table

 


 

P-value

 


 

Question 2

 

A random sample of 150 Introductory Stats students last semester at MSVU were

 

separated based on gender (male or female) and then asked what kind of car they have

 

(domestic, foreign or unknown). Only students who have a car are included here.

 

Type of Car

 

Foreign

 

I don?t know

 


 

Gender

 


 

Domestic

 


 

Female

 


 

46

 


 

49

 


 

17

 


 

Male

 


 

11

 


 

24

 


 

3

 


 

Row Total

 


 

a. Complete the table above by filling in the row totals.

 

b. For the females in the sample, the distribution of Type of Car is provided. Complete

 

the table below by calculating the distribution of Type of Car for the males.

 


 

Gender

 

Female

 


 

Type of car

 

Foreign

 

49/112 =

 

43.75%

 


 

Domestic

 

46/112 =

 

41.07%

 


 

Male

 


 

I don?t know

 

17/112 =

 

15.18%

 


 

Row

 

Total

 

100%

 

100%

 


 

c. For the individuals who are female, the bar chart of the distribution of their Type of

 

Car is provided. For the males, draw a bar chart for the distribution of Type of Car.

 

Make sure to use percentages and use the same scale as the graphs provided to

 

make your comparisons easier. Remember to label your graphs clearly. You need to

 

add the appropriate labels to the graphs that were provided. Be sure to give each

 

chart a title, include variable names, and label both the horizontal and vertical axes.

 


 

Distribution of Type of Car for Females

 

70

 

60

 


 

Percent

 


 

50

 

40

 

30

 

20

 

10

 

0

 


 

Domestic

 


 

Foreign

 


 

I don't know

 


 

Type of Car

 


 

d. Based on the graphs in part (c), what

 

can you say about the association between gender and type of car? Circle one of the

 

following:

 


 

No association

 


 

Moderate Association

 


 

Strong Association

 


 

e. Explain, with specific reference to the graphs in part (c), your answer to part (d).

 


 

Determine if the data provide evidence at a 5% significance level that gender is

 

independent of type of car. Use the Minitab Output below to help you answer the

 

following questions.

 

Chi-Square Test for Association: Gender, Type of Car

 

Rows: Gender

 


 

Columns: Type of Car

 


 

Domestic

 


 

Foreign

 


 

I Dont

 

Know

 


 

Female

 


 

46

 

42.56

 

0.2780

 


 

49

 

54.51

 

0.5563

 


 

17

 

14.93

 

0.2860

 


 

112

 


 

Male

 


 

11

 

14.44

 

0.8195

 


 

24

 

18.49

 

1.6397

 


 

3

 

5.07

 

0.8430

 


 

38

 


 

57

 


 

73

 


 

20

 


 

150

 


 

All

 


 

Cell Contents:

 


 

All

 


 

Count

 

Expected count

 

Contribution to Chi-square

 


 

Pearson Chi-Square = 4.423, DF = 2, P-Value = 0.110

 


 

f. On the Minitab output above, circle or highlight the number of female students in the

 

sample who have a domestic car.

 

g. Is this a test of homogeneity or independence? Explain in context.

 


 

h. The independence assumption is met. Is the expected cell condition met? Explain.

 


 

i. State the appropriate hypotheses in plain English, in the context of the problem.

 


 

j. For the female students who said their car is a domestic model, state the expected

 

value and the chi-squared contribution (from the output) and show how each are

 

calculated.

 

Expected Value: __________________

 


 

?2 Contribution: _________________

 


 

Expected Value

 

Formula

 


 

Values filled in

 


 

?2 Contribution

 

Formula

 


 

Values filled in

 


 

k. What is the value of the test statistic?

 


 

_________________

 


 

l. Calculate the degrees of freedom and report the P-value from the table in your text

 

AND the output.

 

Degrees of freedom: ______________________

 

Value(s) from Table: ______________________

 

P-value from the Table: ____________________

 

P-value from the output: ____________________

 

m. Briefly assess the strength and significance of the evidence.

 

Strength:

 

Significance:

 


 

n. State your conclusion in the context of the problem.

 


 

Question 3

 

Turn to page 258 of your textbook and read the story for question 18. For the purpose of

 

this lab, we will be looking at the data for the Australian Crocodiles only. Use the Minitab

 

output, and the graphs provided on the last page of this lab, to answer the following

 

questions.

 

a. Based on the fitted line plot, do you think head size is a good predictor of body

 

length? Explain.

 


 

b. State the least-squares regression line relating predicted body length and head size.

 


 

c. Use the regression equation to find the predicted body length, ?, for observation 9

 

(the crocodile with a head size of 52 cm).

 


 

Head size = ___________

 


 

Predicted body length = ___________

 

(Don?t forget to state your units.)

 


 

Circle the predicted value on the output and record it here: ______________

 

d. Calculate the residual for observation 7 by hand:

 

Residual = ___________ = _____________

 

(formula)

 


 

Answer: __________

 


 

(calculation)

 


 

Now circle the residual on the Minitab output.

 

Copy the Minitab value here: ______________

 

e. The sample slope is __________. Interpret this value in the context of the problem.

 


 

Minitab Output:

 

Regression Analysis: Body versus Head

 

Analysis of Variance

 

Source

 

Regression

 

Head

 

Error

 

Lack-of-Fit

 

Pure Error

 

Total

 


 

DF

 

1

 

1

 

13

 

10

 

3

 

14

 


 

Adj SS

 

95610.2

 

95610.2

 

1837.2

 

1589.7

 

247.5

 

97447.4

 


 

Adj MS

 

95610.2

 

95610.2

 

141.3

 

159.0

 

82.5

 


 

F-Value

 

676.54

 

676.54

 


 

P-Value

 

0.000

 

0.000

 


 

1.93

 


 

0.321

 


 

Model Summary

 

S

 

11.8879

 


 

R-sq

 

98.11%

 


 

R-sq(adj)

 

97.97%

 


 

R-sq(pred)

 

97.45%

 


 

Coefficients

 

Term

 

Constant

 

Head

 


 

Coef

 

-21.3

 

7.828

 


 

SE Coef

 

12.9

 

0.301

 


 

T-Value

 

-1.65

 

26.01

 


 

P-Value

 

0.123

 

0.000

 


 

Regression Equation

 

Body = -21.3 + 7.828 Head

 

Fits and Diagnostics for All Observations

 

Obs

 

1

 

2

 

3

 

4

 

5

 

6

 

7

 

8

 

9

 

10

 

11

 

12

 

13

 

14

 

15

 


 

Body

 

161.00

 

179.00

 

226.00

 

259.00

 

287.00

 

300.00

 

342.00

 

333.00

 

406.00

 

459.40

 

376.20

 

380.00

 

265.00

 

349.00

 

263.60

 


 

Fit

 

166.52

 

166.52

 

229.14

 

252.62

 

291.76

 

291.76

 

338.73

 

354.38

 

385.69

 

452.23

 

375.52

 

397.43

 

272.98

 

337.94

 

272.98

 


 

Resid

 

-5.52

 

12.48

 

-3.14

 

6.38

 

-4.76

 

8.24

 

3.27

 

-21.38

 

20.31

 

7.17

 

0.68

 

-17.43

 

-7.98

 

11.06

 

-9.38

 


 

Std Resid

 

-0.54

 

1.23

 

-0.28

 

0.56

 

-0.42

 

0.72

 

0.29

 

-1.89

 

1.84

 

0.72

 

0.06

 

-1.59

 

-0.70

 

0.97

 

-0.82

 


 

VIF

 

1.00

 


 

Fitted Line Plot

 

Body = - 21.34 + 7.828 Head

 

500

 


 

S

 

11.8879

 

R-Sq

 

98.1%

 

R-Sq(adj) 98.0%

 


 

450

 


 

Body

 


 

400

 

350

 

300

 

250

 

200

 

150

 

20

 


 

30

 


 

40

 


 

Head

 


 

50

 


 

60

 


 

 


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