Question

Let μ denote the true average lifetime for a certain type of pen under controlled laboratory conditions. A test of H₀: μ = 10 versus H_a: μ < 10 will be based on a sample of size 36. Suppose that σ is known to be 0.6, from which σ_x = 0.1. The appropriate test statistic is then

Answer the following questions using Table 2 in Appendix A.

(a) What is α for the test procedure that rejects H₀ if z ≤ -1.26? (Give answer to 4 decimal places.)
α =  

(b) If the test procedure of Part (a) is used, calculate β when μ = 9.8. (Give answer to 4 decimal places.)
β =

(c) Without doing any calculation, explain how β when μ = 9.5 compares to β when μ = 9.8.
β when μ = 9.5 would be  ---Select--- smaller larger  than β when μ = 9.8.

Check your assertion by computing β when μ = 9.5.
β =  

(d) What is the power of the test when μ = 9.8? (Give answer to 4 decimal places.)

Answer 1