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 H 0: p = 0.15 versus H a : p > 0.15. What is the test statistic?

Question

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dfbustos dfbustos · Answer 1 · 2020-05-06T04:51:24+02:00

Answer:

[tex]z=\frac{0.21 -0.15}{\sqrt{\frac{0.15(1-0.15)}{100}}}=1.68[/tex]

Step-by-step explanation:

Information provided

n=100 represent the random sample taken

X=21 represent the number of bags overfilled

[tex]\hat p=\frac{21}{100}=0.21[/tex] estimated proportion of overfilled bags

[tex]p_o=0.15[/tex] is the value that we want to test

z would represent the statistic

Hypothesis

We need to conduct a hypothesis in order to test if the true proportion of overfilled bags is higher than 0.15.:

Null hypothesis:[tex]p =0.7[/tex]

Alternative hypothesis:[tex]p > 0.15[/tex]

The statistic for this case is:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)

And replacing the info given we got:

[tex]z=\frac{0.21 -0.15}{\sqrt{\frac{0.15(1-0.15)}{100}}}=1.68[/tex]