You wish to conduct the following hypothesis test at 5% significance level :
?0: ?=5 vs. ?1: ?<5
A simple random sample with 16 observations has been collected. You can assume normal population with standard deviation equal to 0.1. The power of the z-test, calculated at ?1=5, equals:?
I have started off by finding the rejection region, P (Z<-1.645) = 0.05, so the rejection region is R = (x̄ < 4.958875)
I am now having trouble calculating the power of the test, without having a value for x̄?
The question asks you to calculate the power at 1=5 but this wouldn't make sense since the power of a test is the probability of detecting a false null hypothesis, but this would mean that the null hypothesis is true and the concept of power doesn't make sense? Help would be very much appreciated thank you!
?0: ?=5 vs. ?1: ?<5
A simple random sample with 16 observations has been collected. You can assume normal population with standard deviation equal to 0.1. The power of the z-test, calculated at ?1=5, equals:?
I have started off by finding the rejection region, P (Z<-1.645) = 0.05, so the rejection region is R = (x̄ < 4.958875)
I am now having trouble calculating the power of the test, without having a value for x̄?
The question asks you to calculate the power at 1=5 but this wouldn't make sense since the power of a test is the probability of detecting a false null hypothesis, but this would mean that the null hypothesis is true and the concept of power doesn't make sense? Help would be very much appreciated thank you!