5.

[4] Teachers want to know which night each week their students are doing most of their homework. Most teachers think that students do homework equally throughout the week. Suppose a random sample of 56 students were asked on which night of the week they did the most homework. The results were distributed as in table below. _mm-mm Number of ------- From the population of students, do the nights for the highest number of students doing the majority of their homework occur with equal frequencies during a week? What type of hypothesis test should you use? Assume any missing information. 6. [5] In the table below, the height (sidewalk to roof) of notable tall buildings in America is compared with the number of stories of the building (beginning at street level). Height (in feet) Stories 1,050 57 428 28 362 26 529 40 790 60 401 22 380 38 1,454 110 1,127 100 700 46 a. Using stories as the independent variable and height as the dependent variable, make a scatter plot of the data. Does it appear from inspection that there is a relationship between the variables? b. Find and interpret the correlation coefficient. c. Calculate the least-squares line. Put the equation in the form y = a + bx. d. Find the estimated heights for a building that has 32 stories and for a building that has 94 stories. e. Based on the least-squares line, adding an extra story is predicted to add about how many feet to a building?7. [4] The following output is associated with a multiple regression model with three independent variables: df SS MS F Regression 3 16,646.091 5,548.697 5.328 Residual 21 21,871.669 1,041.508 Total 24 38,517.760 Coefficients Standard Error t Stat p-value Intercept 87.790 25.468 3.447 0.002 X1 -0.970 0.586 -1.656 0.113 0.002 0.001 3.133 0.005 X3 -8.723 7.495 -1.164 0.258Lower 95% Upper 95% Intercept 34.827 140.753 X 1 -2.189 0.248 * 2 0.001 0.004 X3 -24.311 6.864 Use a = 0.05, where necessary. a. What is the regression model associated with these data? b. Conduct a global F-test. Is the model statistically significant? c. How much of the variation in the dependent variable can be explained by the model? d. Are all of the independent variables in the model significant? If not, which are not and how can you tell? e. How much of a change in the dependent variable will be associated with a one-unit change in X2? In X3? f. Do any of the 95% confidence interval estimates of the slope coefficients contain zero? If so, what does this indicate