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?

We have a large sample size n = 100, the point estimate for the true proportion of overfilled bags p is given by [tex]\hat{p} = 21/100[/tex]. The test statistic is given by [tex]Z=\frac{\hat{p}-0.15}{\sqrt{0.15(0.85)/100}}[/tex] 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 [tex]z=\frac{0.21-0.15}{\sqrt{0.15(0.85)/100}} = 1.68[/tex]

topeadeniran2 topeadeniran2 · Answer 2 · 2022-04-05T17:37:00+02:00

The test statistic from the information about the chips company will be 1.68.

How to compute the test statistics?

Firstly, the sample proportion will be = 21/100 = 0.21

The claimed proportion = 0.15

Significance level = 0.05

Standard deviation will be:

= [✓0.15 × ✓0.85 / ✓100]

= 0.036

Therefore, the test statistic will be:

= [(0.21) - 0.15] / 0.036

= 1.68

In conclusion, the test statistic is 1.68.

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