Question

2. (2 pts) For the following scenarios, • describe what the mean parameter µ represents in each scenario, and • set up H0 and Ha related to µ (i.e. What hypotheses would you test to assess the specification/claim/belief?) Do not perform the hypothesis tests. a.

A random sample of 30 pieces of acetate fiber has a sample mean absorbency of 15% with a sample standard deviation of 1.5%. Is there strong evidence that this fiber has a true mean absorbency of less than 18%?

b. A manufacturer of a synthetic fishing line claims that its product has an exact mean breaking strength of 9 kilograms (no more, no less). A fishing fanatic takes a random sample of n=20 fishing line specimens and computes a sample average strength of 8.5 kilograms with sample standard deviation of 0.65 kilogram. Is there strong evidence that the mean breaking strength is 9 kg?

For part b, notice the the evidence we're looking for is 9 kg; it's not bigger or less.

Answer 1

Solution:

We have to describe the mean parameter µ and set up H0 and Ha related to µ.

Part a)

Given: We have to test if there is strong evidence that this fiber has a true mean absorbency of less than 18%.

That is we have to test if population mean µ is less than 18%.

Thus:

The mean parameter µ is: Population mean absorbency acetate fiber = µ = 18%

and Since we have to test true mean absorbency of less than 18%, this is left tailed test.

Thus Hypothesis H0 and Ha are:

Vs  

Part b)

Given: We have to test if there is strong evidence that the mean breaking strength is 9 kg.

Thus:

The mean parameter µ is: the population mean breaking strength = µ = 9 kg.

Since hypothesis statement stated in question is non-directional, that is , it does not say whether it is less than 9 kg or greater than 9kg. Thus this is two tailed test.

Thus Hypothesis H0 and Ha are:

   Vs