Question

A quality control engineer at a potato chip company tests the bag filling machine by weighing bags of potato chips. Not every bag contains exactly the same weight. But if more than 15% of bags are over-filled then they stop production to fix the machine. They define over-filled to be more than 1 ounce above the weight on the package. The engineer weighs 100 bags and finds that 21 of them are over-filled. He plans to test the hypotheses: H0: p = 0.15 versus Ha: p > 0.15 (where p is the true proportion of overfilled bags). What is the test statistic?

Answer 1

Answer:

The test statistic is $Z=\frac{\hat{p}-0.15}{\sqrt{0.15(0.85)/100}}$ and the observed value 1.68

Step-by-step explanation:

We have a large sample size n = 100, the point estimate for the true proportion of overfilled bags p is given by $\hat{p} = 21/100$. The test statistic is given by $Z=\frac{\hat{p}-0.15}{\sqrt{0.15(0.85)/100}}$ which is distributed as a standard normal variable approximately because we have a large sample. The observed value for the test statistic in this case is $z=\frac{0.21-0.15}{\sqrt{0.15(0.85)/100}} = 1.68$