ONLY ANSWER PART C, D AND E
1A. Suppose The lifetime for a competing brands of tires areindependent of each other and approximately normal with unknownmeans but known variances
σ^2= 975 miles^2 and σ^2= 965 miles^2. We gather did sometesting under controlled conditions and have the following summarystatistics:
n1= 75
Ì„x1= 3251.4
n2= 60
Ì„x2= 3274.7
Construct a 80% confidence interval for the difference inpopulation means,μ1−μ2.
B.Using the same setup as part A, conduct a hypothesis test tocheck if the means are equal. Use α= 0.2.
C.Using the same setup as part A, but now assuming we do notknow the variances but assume they are equal. Construct a 99%confidence interval for the difference in means using the samesample data as before. We now know that the sample variances ares^2= 982.2 and s^2= 967.4.
D.Using the same setup as part C, construct a 90% confidenceinterval for the ratio of variances σ^2/ σ^2.
E. Using the same setup as part C, conduct a hypothesis test totest whether population 1 has a smaller variance than population 2using α= 0.1.
