An experiment was conducted to determine the extent to which the growth rate of a certain fungus could be affected by filling test tubes containing the same medium at the same temperature with different inert gases. Three such experiments were performed for each of six gases, and the average growth rate over these three tests was used as the response. The following table gives the molecular weight (X) of each gas used and the average growth rate (Y) in milliliters per hour for the three tests.

a. Find the least-squares estimates of slope and intercept for the straight-line regression of Y on X, and draw the estimated straight line on a scatter diagram for this data set.
b. Test for significant slope of the fitted straight line.
c. What information has not been used that might improve the sensitivity of the analysis?
d. What is the 90% confidence interval for the true average growth rate if the gas used has a molecular weight of 100?
e. Why would it be inappropriate to use the fitted line to estimate the growth rate of a gas whose molecular weight is 200?
f. Based on the choice of X-values used in this study, how would you criticize the accuracy of prediction obtained in this experiment by using the fitted straight line?

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Gas Average Growth Rate (Y) Molecular Weight X) 3.85 3.48 3.27 3.08 2.56 2.21 4.0 20.2 28.2 39.9 83.8 131.3