Since we have a 95 confidence interval the probability or ri

Since we have a 95% confidence interval, the probability or risk of error is 5% or .05. Do you retain or reject the null hypothesis at the alpha = .05 level? Why? retain (fail to reject) since the test value mu = 20 lies in the interval reject eject since the test value mu = 20 does NOT lie in the interval.

Solution

95% confidence interval means , we can say with 95% confidence that the test value m=20 lies in the interval...

so, there is 5% chance of error that it is not in this interval.right!..so, probability of risk or error =0.05.....

now, 95% confidence interval = [ 20 - ( z-score* s.d ) . 20 + ( z-score * s.d) ]..

which certainly contains the pt. 20...so, we retain(fail to reject) because m=20 lies in this interval!