Question 10.15

10.15 Public university tuition: 2008 versus 2013.

Table 10.3 shows the in-state undergraduate tuition and required fees in 2008 and in-state tuition in 2013 for 33 public universities.9

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Table 10.4: TABLE 10.3 In-state tuition and fees (in dollars) for 33 public universities
School 2008 2013 School 2008 2013 School 2008 2013
Penn State 13,706 15,562 Ohio State 8,679 9,168 Texas 8,532 9,790
Pittsburgh 13,642 15,730 Virginia 9,300 9,622 Nebraska 6,584 6,480
Michigan 11,738 12,800 California–Davis 9,497 11,220 Iowa 6,544 6,678
Rutgers 11,540 10,356 California–Berkeley 7,656 11,220 Colorado 7,278 8,056
Michigan State 10,690 12,622 California–Irvine 8,046 11,220 Iowa State 5,524 6,648
Maryland 8,005 12,245 Purdue 7,750 9,208 North arolina 5,397 5,823
Illinois 12,106 11,636 California–San Diego 8,062 11,220 Kansas 7,042 8,790
Minnesota 10,634 12,060 Oregon 6,435 8,010 Arizona 5,542 9,114
Missouri 7,386 8,082 Wisconsin 7,569 9,273 Florida 3,256 4,425
Buffalo 6,385 5,570 Washington 6,802 11,305 Georgia Tech 6,040 7,718
Indiana 8,231 8,750 UCLA 8,310 11,220 Texas A&M 7,844 5,297
  1. Plot the data with the 2008 tuition on the axis and describe the relationship. Are there any outliers or unusual values? Does a linear relationship between the tuition in 2008 and 2013 seem reasonable?
  2. Run the simple linear regression and give the least-squares regression line.

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  3. Obtain the residuals and plot them versus the 2008 tuition amount. Is there anything unusual in the plot?
  4. Do the residuals appear to be approximately Normal? Explain.
  5. Give the null and alternative hypotheses for examining if there is a linear relationship between 2008 and 2013 tuition amounts.
  6. Write down the test statistic and -value for the hypotheses stated in part (e). State your conclusions.

10.15

(a) The relationship is linear, positive, and strong. There are no outliers; a linear model seems reasonable. (b) . (c) The plot looks random and scattered, there is nothing unusual in the plot, and the assumptions appear valid. (d) The distribution is Normal. (e) . (f) . The data show a significant linear relationship between Y2013 and Y2008 tuitions.