Question

1. Holly checks iPhones coming out of assembly for quality. It is assumed that about μ = 0.02% of all iPhones coming out of assembly are defective, and this is a low enough number that they can deal with the defective iPhones at their retail stores. If the rate of defective iPhones is higher, they might need to change their manufacturing process. Holly takes a sample of 1000 iPhones, finds that x = 0.1% of them are defective and tests this against the null hypothesis of H0 : μ = 0.02%. She wants to use a significance of α = 0.001, to be extra certain, and finds that p = 0.05 so she does not reject the null Hypothesis. It turns out later, however, that they realize there was actually a discrepancy with her data and the updated μ-value is now μ = 0.08%. What type of error did Holly make?

Answer 1

Given that, the null hypothesis is : H0 : μ = 0.02%

p-value = 0.05

Since, p-value is greater than significance of α = 0.001, we fail to reject the null hypothesis. It turns out later, however, that they realize there was actually a discrepancy with her data and the updated μ-value is now μ = 0.08%.

In this case they do not reject the null hypothesis, in fact null hypothesis is false. That means they make Type II error.

Answer :. Type II error

Note :

Type II Error : Do not reject H0, when it is false.