The effect of manganese (Mn) on wheat growth is examined in the article “Manganese Defic...

The effect of manganese (Mn) on wheat growth is examined in the article “Manganese Deficiency and Toxicity Effects on Growth, Development and Nutrient Composition in Wheat” (Agronomy Journal [1984]: 213– 217). A quadratic regression model was used to relate y plant height (cm) to x log (added Mn), with μM as the units for added Mn. The accompanying data were read from a scatterplot in the article. Also given is Minitab output, where x₁ = x and x₂= x². Use a .05 significance level for any hypothesis tests needed to answer the questions that follow.

a. Is the quadratic model useful for describing the relationship between y and x?

b. Are both the linear and quadratic predictors important? Could either one be eliminated from the model? Explain.

c. Give a 95% confidence interval for the mean y value when x = 2. The estimated standard deviation of a + b₁ (2)+ b₂ (4) is 1.037. Interpret the resulting interval.

d. Estimate the mean height for wheat treated with 10 mM of Mn using a 90% interval. (Note: The estimated standard deviation of a + b₁ (1)+ b₂ (1) is 1.031 and log(10) = 1.)