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 16% 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 94 bags and finds that 16 of them are over-filled. He plans to test the hypotheses H 0 : p = 0.11 versus H a : p > 0.11. What is the test statistic?

Answer 1

Answer:

The test statistic is z = 1.865.

Step-by-step explanation:

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

H0: p = 0.11

This means that 0.11 is tested at the null hypothesis, and so:

$\mu = 0.11$

$\sigma = \sqrt{0.11*0.89} = 0.3129$

The engineer weighs 94 bags and finds that 16 of them are over-filled.

This means that:

$n = 94, X = \frac{16}{94} = 0.1702$

What is the test statistic?

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.1702 - 0.11}{\frac{0.3129}{\sqrt{94}}}$

$z = 1.865$

The test statistic is z = 1.865.