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Stat 3006: Statistical Methods II

2020 Fall

Practice Midterm 2

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Page 2

Part I Multiple Choice (40 points total) (5 points each)

Please write down your answers in the “Answer Table”! Only answers in the “Answer Table”

will be accepted.

Answer Table

1. 2. 3. 4. 5. 6. 7. 8.

1. A study compares three levels of Factor A and two levels of Factor B, with five

observations in each cell. What are the degrees of freedom for the F statistic that is used

to test for interaction?

A) 2 and 24

B) 3 and 30

C) 5 and 6

D) 6 and 24

2. A study compares three levels of Factor A and four levels of Factor B, with seven

observations in each cell. What are the degrees of freedom for the F statistic that is used

to test for the main effect of Factor B?

A) 3 and 36

B) 3 and 72

C) 4 and 72

D) 4 and 84

3. Consider the following graphic results from a two-way ANOVA. These results show

__________.

A) no significant main effects or interaction effects.

B) a possible significant main effect for factor A and no other significant effects.

C) a possible significant main effect for factor B and no other significant effects.

D) a significant interaction effect and no other significant effects.

Page 3

4. With which of the following research questions could you use a two-way ANOVA

model for the analysis?

A) Is your score on the midterm exam a good predictor of your score on the final

exam?

B) Do your level of stress (high or low) and level of close friendships (several close

friends or few close friends) effect the number of days you are sick each year?

C) Does the number of days you exercise per week effect your weight lose?

D) Do your favorite color (red, green, blue, or pink) and your weight (overweight,

underweight, or appropriate weight) determine whether your first child will be a

boy or girl?

5. When examining a scatterplot for strength, you are looking to see _______.

A) how close the points in the scatterplot follow a line

B) how close the points in the scatterplot follow a curve

C) All of the above

D) None of the above

6. The statistical model for simple linear regression has the form

i i i 0 1 y x = + + , i = 1,

2, …, n. Which of the following statements about this statistical model is/are TRUE?

are assumed to be Normally distributed with a mean of 0 and a standard

deviation of .

E) All of the above are true.

Page 4

7. The data referred to in this question were collected on 41 employees of a large

company. The company is trying to predict the current salary of its employees from

their starting salary (both expressed in thousands of dollars). The SPPS regression

output is given below as well as some summary measures:

What is an approximate 95% confidence interval for the slope 1?

A) (–7.57, 4.39)

B) (–4.52, 1.34)

C) (1.80, 2.41)

D) (1.95, 2.26)

Page 5

8. The data referred to in this question were collected on 41 employees of a large

company. The company is trying to predict the current salary of its employees from

their starting salary (both expressed in thousands of dollars). The SPPS regression

output is given below as well as some summary measures:

John Doe works for this company. He started with a salary of $15,300. Predict his

current salary with a 90% confidence interval. Express the interval in the appropriate

units.

A) ($15,683; $45,537)

B) ($18,204; $43,015)

C) ($28,580; $32,640)

Page 6

Part II Analytic Questions (60 points total)

You must show your work to receive full credits. Failure to provide (calculation) steps will result

in deduction in credits.

9. (30 points)

The following partial ANOVA table was obtained from a 2-way ANOVA where three

advertisements were being compared among men and women. A total of 30 males and 30

females were sampled, and 10 of each were exposed to ads 1, 2, and 3, respectively. A

measure of attitude toward the brand was obtained for each subject. An uncompleted

ANOVA table is seen below.

Complete the ANOVA table by filling in the “?” with the appropriate values;

Part b. (6 points)

Write an ANOVA model describing this situation. What is the distribution assumption of the

error terms?

Page 7

Part c. (8 points)

What are the assumptions for the ANOVA model? How do you check these assumptions?

Part d. (5 points)

Perform a hypothesis testing whether the ad effects differ among the genders (and vice versa)

(α =0.05), and state your conclusion.

Page 8

10. (30 points) The adjacent data name the coal producing counties in Northeastern

Pennsylvania. It shows the number of employees working in coal production in

that county and gives the number (in thousands) of tons of bituminous coal

produced. The data are fitted by simple linear regression using R. The part of

outputs is shown below. The scatter plot for this data is also given below.

Table 1: Analysis of Variance

Source DF Sum of Squares Mean Square F Ratio

Model (A) 33316305 (D) (F)

Error (B) 10943695 (E)

Total (C) 44260000

Table 2: Parameter Estimates

Term Estimate Std Error t Ratio Prob>|t|

Intercept 544.77 918.85 (G) 0.5749

Ratio 5.24 1.22 (H) 0.0052

Part a. (6 points)

Write the simple linear regression model. Identify the variables and parameters. Find the

estimates for these parameters.

Page 9

Part b. (6 points)

Find the regression equation. Which method can be used to find the regression equation?

Explain this method.

Part c. (8 points)

The values missing from these two tables are:

Page 10

Part d. (5 points)

The researcher doubts if there is any relationship between the regressor and the response. So

he performs a test on the slope at a significant level 0.05. What is the appropriate hypothesis

and what test statistic should be used? And make conclusion based on the results. (α = 0.05).

Part e. (5 points)

Construct a 98% CI for the intercept.

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