Question: Physical Sciences Tinted residential windows have become popular because they help a home absorb solar energy, keep out harmful ultraviolet rays, and add privacy. Two independent random samples of tinted windows were obtained, each produced by applying a thin film of a specified color and density. The shading coefficient of each tinted window (a unitless quantity) was measured, and the summary statistics are given in the following table.
Assume the underlying populations are normal and the population variances are equal.
a. Is there any evidence to suggest the population mean shading coefficients are different? Use a = 0.01.
b. Construct a 99% confidence interval for the difference in population mean shading coefficients, μ1 - μ2.
c. Use the confidence interval in part (b) to determine whether there is any evidence to suggest the shading coefficients are different. Does your answer agree with part (a)? If so, why? If not, why not?