1. A researcher believes that the engagement level of native students in PhD programs of Canada is less than international students. To test this hypothesis data was collected from a group of international students and native students. Data is represented in the following table:

Engagement

Group of Students

High

Low

Total

International students

200

100

300

Native students

250

150

400

Test the hypothesis in 99% confidence level.

2. A researcher believes that 60% of managers in Canada have Visionary Management Style. To test this hypothesis, she collects a random sample of 200 mangers and realizes half of them follow Visionary Management Style. Test the hypothesis with 5% level of significance.

3. A researcher wishes to investigate the relationship amongst the distance between a house and the closest fire station in kilometers X (independent variable) and the damage that fire caused to them in thousand dollars as a dependent variable Y.A sample of houses from different parts of the city is randomly selected and the results are summarized in the ANOVA table below:

Degrees of Freedom

SS

Regression

1

841.77

Residual

13

69.75

Total

14

911.52

Coefficients

Standard Error

t Stat

p-value

Intercept

10.28

1.42

7.24

0.006

X variable

4.92

0.39

12.53

0.001

a. What is the estimated regression equation that relates the fire damage (Y) to the distance from the fire station (X)?

b. If a property is 5.8 kilometers away from the closest fire station what is the estimated damage in thousands of dollars?

c. Is the regression relationship significant? Use the p-value approach and 1% level of significance.

d. Compute the coefficient of determination between distance and the fire damage. Interpret the result in the context of the problem.