For the following scenarios, describe what the mean (mu) represents, and set up

Question

For the following scenarios,

describe what the mean (mu) 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. 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%?
b. 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.

Explanation / Answer

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]

*******************

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]

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