Manufacturing and Product Development A study was conducted to determine the effect of thread…
Manufacturing and Product Development A study was conducted to determine the effect of thread count (x1) and the percentage of cotton (x2) on the lifetime of standard twin bed sheets (y, in years). A machine was constructed to simulate continued usage and to allow a measurement of the lifetime.
a. Estimate the regression coefficients in the model
b. Construct an ANOVA table and conduct a model utility test. Use technology to find the p value associated with this test. Find the value of r2. Explain the meaning of this value.
c. Conduct the necessary hypothesis tests to determine whether both predictor variables are significant. Use an overall significance level of a = 0.05.
d. Find a 99% prediction interval for an observed value of y for x1 = 320 and x2 = 100.
e. Suppose a certain brand of bed sheets is sold with 50% cotton and various thread counts. What thread count would guarantee an estimate of the mean lifetime of at least 15 years?