It may be assumed that the length of nails produced by a particular machine is a normally distributed random variable with standard deviaiton 0.02cm. The lengths of a random sample of 5 nails are 1.14cm, 1.15cm, 1.14cm, 1.12cm and 1.16cm.
a) Test, at the 5% significance level, the hypothesis that the machine produces nails with a mean length of 1.12cm.
b) Find the probability of committing a Type II error when the true mean length is 1.14cm.
For a), I said that it was two-sided, with:
Null hypothesis H0: mu=1.12, Alternative hypothesis H1: mu is not equal to 1.12. Is this correct?
For b), I know that P(Type II error)= 1 - Power, where Power= Pr(Null hypothesis is rejected). What I was confused about was whether the test was one-sided or two-sided, and how this would affect calculating the probability of a type II error.
Any help would be appreciated