Question

Toughness and fibrousness of asparagus are major determinants of quality. This was the focus of a study

reported in “Post-Harvest Glyphosphate Application Reduces Toughening, Fiber Content, and

Lignification of Stored Asparagus Spears” (J. of the Amer. Soc. Of Horticultural Science, 1988: 569-572).

The article reported the accompanying data on x = shear force (kg) and y = percent fiber dry weight.

X= 46,48,55,57,60,72,81,85,94,109,121,132,137,148,149,184,185,187

Y= 2.18,2.10,2.13,2.28,2.34,2.53,2.28,2.62,2.63,2.5,2.66,2.79,2.8,3.01,2.98,3.34,3.49,3.26

Summary Statistics:

?=18, Σ??=1950, Σ??2=251, 970, Σ??=47.92, Σ??2=130.6075, Σ????=5530.92

(a) Distributional assumptions in regression are based on the assumption that the model error terms

satisfy ??~?(0,?^2), ?=1,2,⋯,?, and are independent. We estimate ? with ? = sqrt(???/?−2). Compute ?

using the given data.

(b) Compute a 99% confidence interval for ?1.

(c) Test the hypothesis ?0: ?1≥.01 versus ?1: ?1<.01 at the ?=.05 level. State your conclusion.

(d) Suppose x=150. Compute a 95% confidence interval for ??|?=150, the population mean percent fiber

dry weight for asparagus with shear force 150 kg. Write an interpretation for this interval.

(e) Suppose x=150. Compute a 95% prediction interval for ?|? = 150, a future value of percent dry

weight for asparagus with shear force 150 kg. Write an interpretation for this interval.

Please show all steps as to how you arrive at the answers

Answer 1