Question

A quality control engineer inspects 300 widgets on an assembly line and finds that 18 are defective. The assembly line should produce defectives at a rate of no more than 5 defectives for every 100 produced. Are the inspector's results that the line should be shut down and repaired? Use alpha=0.01. Could you have made a type 2 error? Why or why not?

P=.2236

please explain in depth about the error. (I already have the problem answered, just confused on the error.

Answer 1

Let p be the true proportion of defectives.

Hypothesized proportion, p = 5/100 = 0.05

Null hypothesis H0: p = 0.05

Alternative hypothesis H1: p > 0.05

Sample proportion, = 18/300 = 0.06

Standard error of proportion, SE = = 0.01258

Test statistic, z = ( - p) / SE = (0.06 - 0.05) / 0.01258 = 0.79

P-value = Probability that line should be shut down and repaired = P(p > 0.06) = P(z > 0.79) = 0.2148

Since P-value is greater than alpha=0.01, we fail to reject H0.

Type 2 error is the probability to fail to reject H0 when in reality H0 is false.

Since we fail to reject H0, we may have made a type 2 error, if in reality H0 is false.