Letdenote the mean lifetime (in hours) for a certain type of battery under controlled laboratory conditions. A test ofH₀:= 10

versusH_a:< 10

will be based on a sample of size 36. Suppose thatis known to be 0.6, so_x= 0.1.

The appropriate test statistic is then

z=x10

0.1

(a)

What isfor the test procedure that rejectsH₀

ifz1.25?

(Round your answer to four decimal places.)

=

(b)

If the test procedure of part (a) is used, calculatewhen= 9.8. (Round your answer to four decimal places.)

=

Interpret this error probability.

This represents the probability the test rejects the null hypothesis when= 9.8.

This represents the probability the test does not reject the null hypothesis when= 9.8.

This represents the probability the test rejects the null hypothesis when= -1.25.

This represents the probability the test rejects the null hypothesis when= 10.

This represents the probability the test does not reject the null hypothesis when= 10.

(c)

Without doing any calculation, explain howwhen= 9.5 compares towhen= 9.8.

when= 9.5 would be

---Select---

smaller

larger

thanwhen= 9.8.

Check your assertion by calculatingwhen= 9.5. (Round your answer to four decimal places.)

=

(d)

What is the power of the test when= 9.8? (Round your answer to four decimal places.)

When= 9.5? (Round your answer to four decimal places.)

You may need to use the appropriate table in theappendixortechnologyto answer this question.