Question

ONLY ANSWER PART C, D AND E

1A. Suppose The lifetime for a competing brands of tires are independent of each other and approximately normal with unknown means but known variances

σ^2= 975 miles^2 and σ^2= 965 miles^2. We gather did some testing under controlled conditions and have the following summary statistics:

n1= 75

̄x1= 3251.4

n2= 60

̄x2= 3274.7

Construct a 80% confidence interval for the difference in population means,μ1−μ2.

B.Using the same setup as part A, conduct a hypothesis test to check if the means are equal. Use α= 0.2.

C.Using the same setup as part A, but now assuming we do not know the variances but assume they are equal. Construct a 99% confidence interval for the difference in means using the same sample data as before. We now know that the sample variances are s^2= 982.2 and s^2= 967.4.

D.Using the same setup as part C, construct a 90% confidence interval for the ratio of variances σ^2/ σ^2.

E. Using the same setup as part C, conduct a hypothesis test to test whether population 1 has a smaller variance than population 2 using α= 0.1.

Answer 1

c) we will calculate the pooled variance here

Standard error for the difference is

for 99% confidenceand df = 75+60-2=133

critical T value is

The confidence interval is

x1= 3251.4

̄x2= 3274.7

d)

e)