Question

# Determine the probability of making a Type II error for the following hypothesis test, given that...

Determine the probability of making a Type II error for the following hypothesis test, given that μ=1061 μ=1061.

H0 : μ = 1040

H1 : μ >1040

For this test, take σ=47, n=26, and α=0.07.

P(Type II Error) =

I would really like to understand how to solve this kind of question not just the answer if anyone has the time to explain the logic (and formulas) it would be much appreciated

Type II error is the acceptance of a false null hypothesis.

Now the null hypothesis is ​​​​​​, and population standard deviation is given so we use z test. We first find the value of z and hence sample mean for which we can reject the null hypothesis.

The value of the test static is given by

Since significance level is given to be 0.07, and test is right tailed so critical value is z=1.476

So we reject the null hypothesis if

So we reject the null hypothesis if sample mean is greater than 1053.60

Now if the actual population mean is 1061,

Then probability of type II error is

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