The machine operator responsible for the filling machine suspects that the machine actually works better than stated. By choosing $H _ { 0 } : p \geq 0.3$ as the null hypothesis, he wants to test his suspicion with a sample of 100 bottles. The number of underfilled bottles in the sample is again assumed to be binomially distributed. (1) Determine a decision rule appropriate to the null hypothesis at a significance level of $\alpha = 0.05$. (2) Describe the Type II error in the given context.
The machine operator responsible for the filling machine suspects that the machine actually works better than stated. By choosing $H _ { 0 } : p \geq 0.3$ as the null hypothesis, he wants to test his suspicion with a sample of 100 bottles. The number of underfilled bottles in the sample is again assumed to be binomially distributed.
(1) Determine a decision rule appropriate to the null hypothesis at a significance level of $\alpha = 0.05$.
(2) Describe the Type II error in the given context.