Question 1A A real estate research firm has developed a regression model relating list price (Y in

$1,000) with two independent variables. The two independent variables are number of bedrooms

and size of the property. Part of the regression results are shown below.

ANOVA df SS MS Regression 2 154881.37 77440.69 Residual 57 899723.61 15784.62

Coefficients Standard Error t Stat Intercept 74.298 91.326 # Bedrooms 73.634 25.271 Acres

41.458 38.630

1. What has been the sample size? (2 Points)

n = 57+1 = 58

2. What is the value of the F test statistic for testing whether the regression model is

significant? (2 Points)

3. What is the rejection rule for testing whether the regression model is significant at the 0.05

level of significance? (2 Points)

F > 3.159, reject H0

4. What is the value of the t test statistic for testing whether the variable Acres is significant? (2

Points)

Question 1B A computer manufacturer has developed a regression model relating Sales (Y in

$10,000) with two independent variables. The two independent variables are Price (in dollars)

and Advertising (in $1000). Part of the regression results are shown below.

ANOVA df SS MS

Regression 2 36641630 18320815.0 Residual 39 47277876 1212253.2 Coefficients Standard

Error t Stat Intercept 2169.233 1239.880 Price -0.793 0.324 Advertising 0.221 0.081

1. What has been the sample size? (2 Points)

SAMPLE SIZE=DF(REG)+DF(RES)+1=2+35+1=38

2. What is the value of the F test statistic for testing whether the regression model is significant? (2 Points)

3. What is the rejection rule for testing whether the regression model is significant at the 0.05 level of significance? (2 Points)

4. What is the value of the t test statistic for testing whether the variable Price is significant? (2 Points)

Question 4A A recent market study produced the following data on education level by gender:

Education Level Male Female TOTAL Up to High School 250 350 600 College or U Grad 460

540 1000 Postgraduate 65 85 150 TOTAL 775 975 1750

We want to determine if education level is independent of gender.

1. State the null and alternative hypotheses for a contingency table test if we want to determine if

education level is independent of gender (2 Points)

2. State the rejection rule for the critical value approach. Let alpha = 0.01. (2 Points)

3. Calculate the expected frequency for the cell "Postgraduate" and "Female" (2 Points)

4. If the Chi Square statistic is 2.914 what is your conclusion? (2 Points)

Question 4B Among 1,000 managers with degrees in business administration, the following

data have been accumulated as to their fields of concentration.

Major Top Management Middle Management TOTAL Management 280 220 500 Marketing 120

80 200 Accounting 150 150 300 TOTAL 550 450 1000

We want to determine if the position in management is independent of field (major) of

concentration.

1. State the null and alternative hypotheses for a contingency table test if we want to determine if

the position in management is independent of field (major) of concentration (2 Points)

2. State the rejection rule for the critical value approach. Let alpha = 0.01. (2 Points)

3. Calculate the expected frequency for the cell "Marketing" and "Middle Management" (2

Points)

4. If the Chi Square statistic is 5.253 what is your conclusion? (2 Points)

Question 7A In a completely randomized experimental design, 6 experimental units were used

for each of the 4 levels of the factor (i.e., 4 treatments):

Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between Treatments

14302 (1) (2) (3) Error (Within Treatments) 28019 (4) (5) Total 42321 (6)

1. Fill in the blanks in the following ANOVA table (There are 6 unknown numbers) (2 Points)

2. What is the null and alternative hypothesis for this ANOVA test? (2 Points)

3. Find the critical value of the F test at the 0.05 level of significance. (2 Points)

4. What is the conclusion of the F test? Please give reason. (2 Points)

Question 7B In a completely randomized experimental design, 5 experimental units were used

for each of the 4 levels of the factor (i.e., 4 treatments):

Source of Variation Sum of Squares Degrees of Freedom Mean Square F Between Treatments

4302 (1) (2) (3) Error (Within Treatments) 8019 (4) (5)

Total 12321 (6)

1. Fill in the blanks in the following ANOVA table (There are 6 unknown numbers) (3

Points)

Source of Variation Sum of Squares Degrees of Freedom Mean Square F

Between

Treatments 4302 3 1413 2.861205

Error (Within

Treatments) 8019 16 501.1875

Total 12321

2. What is the null and alternative hypothesis for this ANOVA test? (1 Point)

3)Find the critical value of the F test at the 0.05 level of significance. (2 Points)

Given a=0.05, the critical value is F(0.95, df1=3, df2=16) =3.24 (from F table)

4. What is the conclusion of the F test? Please give reason. (2 Points)

Since F=2.861205 is less than 3.24, we do not reject the null hypothesis.