State the assumptions required to perform a Kruskal-Wallis test for a difference between more than two population medians. For the provided data set, assume that all such assumptions hold (verify them where possible.) 6) A fire-science specialist tests three different brands of flares for their burning times (in 6) minutes) and the results are given below. For the sample data, at the 0.05 significance level, test the claim that the three different brands have the same median burn time. State the conclusion from your investigation. Brand X 16.4 17.6 18.3 17.0 17.1 17.3 Brand Y 17.9 18.0 17.8 18.4 17.6 19.0 19.1 Brand Z 17.3 16.4 16.5 16.0 15.8 16.3 17.1 Solve the Problem(s). 7) A national job placement company is interested in developing a model that might be used to explain the variation in starting salaries for college graduates based on their college GPA. The following data were collected through a random sample of the clients with which this company has been associated (Monetary figures given in USD). GPA Starting Salary 3.2 $35,000 3.4 $29,500 2.9 $30,000 3.6 $36,400 2.8 $31,500 2.5 $29,000 3.0 $33,200 3.6 $37,600 2.9 $32,000 3.5 $36,000 Make a scatter plot of the data. Is a linear model suitable? If YES, then determine the least squares linear regression model. Which sample data point has the largest residual? smallest residual? Find the coefficient of correlation. What percentage of the variation in starting salaries is explained by the regression model? Perform a t-test for linear correlation as well as an F-test for correlation. Do the results agree? State the null and alternative hypotheses for these tests. Show all work in the computation of the test statistics or cite any technology used State the conclusions of these investigations. Use the model to predict the starting salary when the GPA is 4.0