. 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.

4. Assume you are working in a data analysis team at a company and you have access to volume of sales data over time. Last month, your company increased its YouTube ads, and the manager of the company thinks that these ads were very successful. One of your team members suggested a regression analysis to see if because of the increased ads, the volume of sales increased last month. What do you think about this suggestion? Assume that you decide to perform the regression analysis, what are the independent and dependent variables in your regression? If you run the regression and you find out that the slope coefficient of the regression is positive, does this necessarily mean your manager was right about the effect of new ads?