Please help me out with the following:
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. 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. BUSI 1013 STATISTICS FOR BUSINESS 10 YORKVILLE UNIVERSITY WWW.YORKVILLEU.CA d. Compute the coefficient of determination between distance and the fire damage. Interpret the result in the context of the