Do not perform the hypothesis tests For the following scenar

Do not perform the hypothesis tests. For the following scenarios, describe what the mean p represents, and set up H0 and Ha related to mu (i.e. What hypotheses would you test to assess the specification/claim/belief?) Do not perform the hypothesis tests. A random sample of 25 pieces of acetate fiber has a sample mean absorbency of 12% with a sample standard deviation of 1.25%. Is there strong evidence that this fiber has a true mean absorbency of less than 20%? A manufacturer of a synthetic fishing line claims that its product has a mean breaking strength of at least 8 kilograms. A random sample of n=9 fishing line specimens yields a sample average strength of 7.5 kilograms with sample standard deviation of 0.65 sec.

Solution

a)

Here, u = the true mean absorbency of acetate fiber

Note that the claim goes to the alternative hypothesis.

Thus,

H0: u > 20%
Ha: u < 20% [ANSWER]

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b)

Here,

u = true mean breaking strength of a manufacturer\'s fishing line

Note that the claim goes to the alternative hypothesis.

As we want to prove the manufacturer wrong, then,

H0: u > 8 kg
Ha: u < 8 kg [ANSWER]