Let u denote the mean lifetime (in hours) for a certain type of battery under controlled laboratory conditions. A test of Ho: H = 10 versus HH< 10 will be based on a sample of size 36. Suppose that o known to be 0.6, so o = 0.1. The appropriate test statistic is then x- 10 (a) What is a for the test procedure that rejects H, if zs -1.447 (Round your answer to four decimal places.) (b) If the test procedure of part (a) is used, calculate B when a= 9.8. (Round your answer to four decimal places.)

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Let u denote the mean lifetime (in hours) for a certain type of battery under controlled laboratory conditions. A test of Ho: µ = 10 versus H,:µ < 10 will be based on a sample of size 36. Suppose that o is known to be 0.6, so o, = 0.1. The appropriate test statistic is then
x- 10
z =
0.1
(a) What is a for the test procedure that rejects H, if z<-1.44? (Round your answer to four decimal places.)
a =
(b) If the test procedure of part (a) is used, calculate B when µ = 9.8. (Round your answer to four decimal places.)
B =
Interpret this error probability.
O This represents the probability the test rejects the null hypothesis when u = 9.8.
O This represents the probability the test does not reject the null hypothesis when u = 10.
O This represents the probability the test does not reject the null hypothesis when u = 9.8.
O This represents the probability the test rejects the null hypothesis when u = 10.
O This represents the probability the test rejects the null hypothesis when u = -1.44.
(c) Without doing any calculation, explain how B when u = 9.5 compares to B when u = 9.8.
B when u = 9.5 would be ---Select--- v than B when u = 9.8.
Check your assertion by calculating B when u = 9.5. (Round your answer to four decimal places.)
B =
(d) What is the power of the test when u = 9.8? (Round your answer to four decimal places.)
When u = 9.5? (Round your answer to four decimal places.)
Transcribed Image Text:Let u denote the mean lifetime (in hours) for a certain type of battery under controlled laboratory conditions. A test of Ho: µ = 10 versus H,:µ < 10 will be based on a sample of size 36. Suppose that o is known to be 0.6, so o, = 0.1. The appropriate test statistic is then x- 10 z = 0.1 (a) What is a for the test procedure that rejects H, if z<-1.44? (Round your answer to four decimal places.) a = (b) If the test procedure of part (a) is used, calculate B when µ = 9.8. (Round your answer to four decimal places.) B = Interpret this error probability. O This represents the probability the test rejects the null hypothesis when u = 9.8. O This represents the probability the test does not reject the null hypothesis when u = 10. O This represents the probability the test does not reject the null hypothesis when u = 9.8. O This represents the probability the test rejects the null hypothesis when u = 10. O This represents the probability the test rejects the null hypothesis when u = -1.44. (c) Without doing any calculation, explain how B when u = 9.5 compares to B when u = 9.8. B when u = 9.5 would be ---Select--- v than B when u = 9.8. Check your assertion by calculating B when u = 9.5. (Round your answer to four decimal places.) B = (d) What is the power of the test when u = 9.8? (Round your answer to four decimal places.) When u = 9.5? (Round your answer to four decimal places.)
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