6 A machine is supposed to produce random digits. Bob thinks that the machine is not fair and that the probability of it producing the digit 0 is less than \(\frac { 1 } { 10 }\). In order to test his suspicion he notes the number of times the digit 0 occurs in 30 digits produced by the machine. He carries out a test at the \(10 \%\) significance level.

1. State suitable null and alternative hypotheses.
2. Find the rejection region for the test.
3. State the probability of a Type I error.
   It is now given that the machine actually produces a 0 once in every 40 digits, on average.
4. Find the probability of a Type II error.
5. Explain the meaning of a Type II error in this context.