J.D. Power and Associates conducts an initial quality study (IQS) each year to determine the quality of newly manufactured automobiles. IQS measures 135 attributes across nine categories, including ride/ handling/braking, engine and transmission, and a broad range of quality problem symptoms reported by vehicle owners. The 2008 IQS was based on responses from more than 62,000 purchasers and lessees of new 2008 model-year cars and trucks, who were surveyed after 90 days of ownership. The data given here portray the industry average of the number of reported problems per 100 vehicles for 1998€“2008.

a. Construct a scatter plot of the number of reported problems per 100 vehicles as a function of the year.
b. Determine if the average number of reported problems per 100 vehicles declines from year to year. Use a significance level of 0.01 and a p-value approach.
c. Assume the relationship between the number of reported problems per 100 vehicles and the year continues into the future. Provide a 95% prediction interval for the initial quality industry average of the number of reported problems per 100 vehicles for 2010.

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Year 998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 Problems 176 167 154 147 133 133 125 2 9 118 18