A researcher wants to study the average lifetime of a certain brand of rechargea

Question

A researcher wants to study the average lifetime of a certain brand of rechargeable batteries I in hours). In testing the hypothesis, Ho: =950 hours vs. H1: 950 hours, a random sample of 25 rechargeable batteries is drawn from a normal population whose standard deviation is 200 hours.

a. Calculate , the probability of a Type II error when =1000 and a=0.10.

b. Calculate the power of the test when =1000 and a=0.10.

c. Interpret the meaning of the power of the test.

d. Recalculate if n is increased from 25 to 40.

e. Review the results of the previous questions. What is the effect of increasing the sample size on the value of ?

f. Recalculate if a is lowered from 0.10 to 0.05.

g. Review the results of the previous questions. What is the effect of decreasing the significance level on the value on ?

Explanation / Answer

This is two tailed test

a) and b)

c)

Power of the test indicates the probability that we make right decision when null is not correct (i.e. we correctly reject it)

d)

e) Power of the test decreae as sample size increases.

mu0 (hypothesised mean) 950 sigma 200 n 25 alpha 0.1 sample/true mean 1000 Std. Error. SE = sigma/sqrt(n) 40.0000 Zcritical -1.645 Xcritical values 884.21 1015.79 Beta or type II error is the probability of fail to reject the null hypothesis P(X<884.21|mu=1000) 0.00190 P(X>1015.79|mu=1000) 0.34648 Hence type II error probability is 0.3484 Power of the test 0.6516

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.