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 High Low Total Group of Students International students 200 100 300 Native students 250 150 400 Test the hypothesis in 99% confidence level.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