Question

Consider the following hypothesis test. H0: μ ≥ 10 Ha: μ < 10 The sample size is 120 and the population standard deviation is 5. Use α = 0.05. If the actual population mean is 9, the probability of a type II error is 0.2912. Suppose the researcher wants to reduce the probability of a type II error to 0.10 when the actual population mean is 10. What sample size is recommended? (Round your answer up to the nearest integer.)

Answer 1

Solution:

Given:

Null and alternative hypotheses:

H0: μ ≥ 10

Ha: μ < 10

Population standard deviation = = 5

Level of significance = = 0.05

Z = 1.645 ...Using excel formula, =ABS(NORMSINV(0.05))

Type II error = = 0.10

Z = 1.28  ...Using excel formula, =ABS(NORMSINV(0.10))

Actual mean = = 9 (It seems you have taken incorrect mean=10 as denominator will become 0)

We have to find sample size.

Formula is:

Calculation:

Hence required sample size = n = 214

Done