Q2. Suppose we wish to test the hypothesis H₁ :u=15; H₁:15 where we know that σ² = 9.0. If the true mean is actually 20, what sample size must be used to ensure that the probability of type II error is no greater than 0.05? Assume a = 0.05.
Sol:-
To solve this problem, we first need to determine the rejection region and the corresponding critical value for the given level of significance α = 0.05. Since this is a two-tailed test, we need to split the α level between the two tails of the distribution.
The rejection region can be expressed as follows:
Reject Ho if Z < -Zα/2 or Z > Zα/2
where Zα/2 is the critical value of the standard normal distribution that corresponds to the upper α/2 percentile. For α = 0.05, Zα/2 = 1.96.
Next, we need to find the sample size n that will ensure that the probability of a type II error is no greater than 0.05, given that the true mean is actually 20. Let us denote the population mean by μ = 20 and the hypothesized mean by μ0 = 15. We also know that the population variance is σ2 = 9.
Step by step
Solved in 2 steps
