Question

Two suppliers manufacture a plastic gear used in a laser printer. A feature important in these gears is the impact resistance, which is measured in pounds per square foot. A random sample of 10 gears supplied by the first supplier gives the following results: x̅̅1̅ = 290 and s1 = 12. A random sample of 15 gears is taken from the second supplier and the results are x̅̅2̅ = 321 and s2 = 15.

a) Is there evidence to supports the claim that the supplier 2 gears has a greater average resistance to impact? Use α = 0.05 and assume that the variances of the two populations are different.

b) Calculate the probability of committing a type II error in a) if the true mean resistances to the Impacts are μ1 = 292 and μ2 = 318 pounds per square foot. Estimate the population variances using the sample variances and use α = 0.05.

c) Does the data support the claim that the average impact strength of the supplier's gears 2 is at least 20 pounds per square foot greater than the one corresponding to supplier 1? Use α = 0.05 and suppose that the variances of the two populations are different.

d) Calculate the probability of committing a type II error in c) if the true average resistance to Impacts are μ1 = 292 and μ2 = 318 pounds per square foot. Estimate the population variances using the sample variances and use α = 0.05.

Answer 1

a)