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algol13
3 years ago
7

Because of variability in the manufacturing process, the actual yielding point of a sample of mild steel subjected to increasing

stress will usually differ from the theoretical yielding point. Let p denote the true proportion of samples that yield before their theoretical yielding point. If on the basis of a sample it can be concluded that more than 20% of all specimens yield before the theoretical point, the production process will have to be modified.
(a) If 9 of 40 specimens yield before the theoretical point, what is the P-value when the appropriate test is used? (Round your answer to four decimal places.) P-value
Mathematics
1 answer:
photoshop1234 [79]3 years ago
4 0

Answer:

P-value ≈ 0.3463

Step-by-step explanation:

Hypothesis test would be

H_{0}:p=0.20

H_{a}:p>0.20

We need to calculate the z-score of sample proportion and then the corresponding P-value.

z-score can be calculated as:

z=\frac{p(s)-p}{\sqrt{\frac{p*(1-p)}{N} } } where

  • p(s) is the sample proportion of specimens yield before the theoretical point (\frac{9}{40}=0.225)
  • p is the proportion assumed under null hypothesis. (0.20)
  • N is the sample size (40)

Using the numbers

z=\frac{0.225-0.2}{\sqrt{\frac{0.2*0.8}{40} } } =0.3953

and the P-value is then P(z)≈0.3463

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