An experiment to investigate the effects of a new technique for degumming of silk yarn was described
Question:
An experiment to investigate the effects of a new technique for degumming of silk yarn was described in the article “Some Studies in Degumming of Silk with Organic Acids” (J. Society of Dyers and Colourists, 1992: 79–86). One response variable of interest was y = weight loss (%). The experimenters made observations on weight loss for various values of three independent variables: x1 = (?C) = 90, 100, 110temperature ; x2 = time of teatment (min) = 30, 75, 120; x3 = tartaric acid concentration (g/L) = 0,8,16. In the regression analyses, the three values of each variable were coded as –1, 0, and 1, respectively, giving the accompanying data (the value y8 = 19.3 was reported, but our value y8 = 20.3 results in regression output identical to that appearing in the article).
a. Does this model specify a useful relationship? State and test the appropriate hypotheses using a significance level of .01.
b. The estimated standard deviation of when x1 =………….. = x9 5 0 (i.e., when temperature = 100, time = 75, and concentration = 8) is 1.248. Calculate a 95% CI for expected weight loss when temperature, time, and concentration have the specified values.
c. Calculate a 95% PI for a single weight-loss value to be observed when temperature, time, and concentration have values 100, 75, and 8, respectively.
d. Fitting the model with only x1, x2, and x3 as predictors gave
.
Does at least one of the second-order predictors provide additional useful information? State and test the appropriate hypotheses.
Introduction to Probability and Statistics
ISBN: 978-1133103752
14th edition
Authors: William Mendenhall, Robert Beaver, Barbara Beaver