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MATH2209 Lab 6

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

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).

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)

(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:

Analysis of Variance

Source

Regression

Error

Lack-of-Fit

Pure Error

Total

DF

1

1

13

10

3

14

95610.2

95610.2

1837.2

1589.7

247.5

97447.4

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%

97.97%

R-sq(pred)

97.45%

Coefficients

Term

Constant

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%

450

Body

400

350

300

250

200

150

20

30

40

50

60

Solution details:
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This question was answered on: Oct 15, 2019

Solution~000.zip (25.37 KB)

STATUS

QUALITY

Approved

Oct 15, 2019

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