According to the National Association of Homebuilders, the average life expectancies of a dishwasher and a garbage disposal are about the same:10 years. Assume that their finding was basedon a sample of n1=60 dishwashers and n2 = 40 garbage disposals, and that the corresponding sample standard deviations were s1 = 3.0 years and s2 = 3.7 years. Using the 0.02 level of significance, examine whether the population standard deviations for the lifetimes of these two types of appliances could be the same.

Question

According to the National Association of Homebuilders, the average life expectancies of a dishwasher and a garbage disposal are about the same:10 years. Assume that their finding was basedon a sample of n1=60 dishwashers and n2 = 40 garbage disposals, and that the corresponding sample standard deviations were s1 = 3.0 years and s2 = 3.7 years. Using the 0.02 level of significance, examine whether the population standard deviations for the lifetimes of these two types of appliances could be the same.

Answer 1

Z = (mean1 - mean2)/standard error (SE) of difference between means

SEdiff = √(SEmean1^2 + SEmean2^2)

SEm = SD/√(n-1)

Since only one SD is provided, you can use just that to determine SEdiff.

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to that Z score. Make your interpretation.