1 It is known that for finishing a laboratory experiment the

1) It is known that for finishing a laboratory experiment the time needed is normally distributed with an average of 80 h. A new setup was designed for the experiment and the average time needed to finish the experiment was found to be 78h for 25 experiments with s =5.2 h. For the claim (that the mean time for the experiment with new set up is smaller than previous setup) to be accepted what should be the probability of a Type I error (?) ?[Do not give ? value as an interval]

Solution

The test statistic is

Z=(xbar-mu)/(s/vn)

=(78-80)/(5.2/sqrt(25))

=-1.92

It is a left-tailed test.

So the probability of a Type I error (?) is

P(Z<-1.92) = 0.0274 (from standard normal table)