I’m mostly confused on how to do part 2 with the hypothesis
testing
Show transcribed image text 5. An investigation is conducted to study gasoline mileage in automobiles when used exclusively for urban driving. Ten properly tuned and serviced automobiles manufactured during the same year are used in the study. Each automobile is driven for 1,000 miles, and the average numbers of miles per gallon (mpg) obtained () and the weight of the automobile in tons (x) are recorded in the following table. It is hypothesized that the average number of mpg is a linear function of the weight of the automobile Car 1 2 3 4 6 8 9 10 Y17.9 16.5 16.4 16.8 18.8 15.517.5 16.4 15.9 18.3 x 1.351.90 1.70 1.80 1.30 2.05 1.60 1.80 1.851.40 (1) Develop the estimated regression line Y = Bo + BX and determine the correlation coefficient r. (2)The r value obtained from (1) seems to suggest the linear dependence of Y and x. Run a hypothesis test to further confirm that Y is indeed a linear function of x as suggested in (1) at α = 0.01. (3) Suppose we are interested in all automobiles weighing 1.7 tons. What is the estimated mpg for these automobiles? Construct a 90% confidence interval on Y = B0 BX at x 1.7 tons. (4) Construct a 90% confidence band for Y = Bo + B:X and plot the results on a graphical paper.
5. An investigation is conducted to study gasoline mileage in automobiles when used exclusively for urban driving. Ten properly tuned and serviced automobiles manufactured during the same year are used in the study. Each automobile is driven for 1,000 miles, and the average numbers of miles per gallon (mpg) obtained () and the weight of the automobile in tons (x) are recorded in the following table. It is hypothesized that the average number of mpg is a linear function of the weight of the automobile Car 1 2 3 4 6 8 9 10 Y17.9 16.5 16.4 16.8 18.8 15.517.5 16.4 15.9 18.3 x 1.351.90 1.70 1.80 1.30 2.05 1.60 1.80 1.851.40 (1) Develop the estimated regression line Y = Bo + BX and determine the correlation coefficient r. (2)The r value obtained from (1) seems to suggest the linear dependence of Y and x. Run a hypothesis test to further confirm that Y is indeed a linear function of x as suggested in (1) at α = 0.01. (3) Suppose we are interested in all automobiles weighing 1.7 tons. What is the estimated mpg for these automobiles? Construct a 90% confidence interval on Y = B0 BX at x 1.7 tons. (4) Construct a 90% confidence band for Y = Bo + B:X and plot the results on a graphical paper.
