Question

Consider the following hypothesis test:

H0:u equal to 25
H1: u> 25
α=0.05, σ= 2.4,n=30

what would be the cutoff value for y mean for the rejection of h0?

If the true value is u=25.75, then what is the power of the test?

Answer 1

Solution:
Given in the question
Null hypothesis H0: mean is equal to 25
Alternate Hypothesis Ha: mean > 25
Here sample size Is large enough and Population standard deviation so we will use Z test
From Z table at alpha = 0.05 and this is right tailed test, so Cutoff value = 1.645
If test stat value is Greater than 1.645 than reject the null hypothesis else we are failed to reject the null hypothesis.

Z = (25.75-25)/2.4/sqrt(30) = 1.712
So from Z table we found p-value
P-value = 0.043
Here we can say that p-value is less than alpha value so we will reject the null hypothesis.