Question: The director of manufacturing at a clothing factory needs to determine whether a new machine is producing a particular type of cloth according to the manufacturer's specifications, which indicate that the cloth should have a mean breaking strength of 70 pounds and a standard deviation of 3.5 pounds.  A sample of 49 pieces of cloth reveals a sample mean breaking strength of 69.1 pounds.

1. Is there evidence that the machine is not meeting the manufacturer's specifications for mean breaking strength (use a 0.05 level of significance)?
2. Compute the p-value and interpret its meaning.
3. What is your answer in (a) if the standard deviation is 1.75 pounds?
4. What is your answer in (a) if the sample mean is 69 pounds and the standard deviation is 3.5 pounds?

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