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-BARSIC- [3]
3 years ago
6

A quality control engineer at a potato chip company tests the bag filling machine by weighing bags of potato chips. Not every ba

g 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?
Mathematics
1 answer:
Ahat [919]3 years ago
5 0

Answer:

z=\frac{0.21 -0.15}{\sqrt{\frac{0.15(1-0.15)}{100}}}=1.68  

Step-by-step explanation:

Information provided

n=100 represent the random sample taken

X=21 represent the number of bags overfilled

\hat p=\frac{21}{100}=0.21 estimated proportion of overfilled bags

p_o=0.15 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:p =0.7  

Alternative hypothesis:p > 0.15  

The statistic for this case is:

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

And replacing the info given we got:

z=\frac{0.21 -0.15}{\sqrt{\frac{0.15(1-0.15)}{100}}}=1.68  

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