Faculty of Engineering and Applied Science
2010 Fall
Tutorial, 2010 November
An existing manufacturing process produces thin wires with a breaking load that is known to be normally distributed with a mean of 100.0 N.
A new process claims to produce thin wires with a greater breaking load. The client will not invest in the new process unless there is clear evidence (at a level of significance of 5%) that the mean breaking load is more than 5 N greater than that of the existing wires.
A random sample of 36 wires has a mean breaking load of 106.0 N, with a sample standard deviation of 3.0 N.
State the appropriate null and alternative hypotheses.
Conduct the appropriate hypothesis test.
Should you advise the client to invest in the new process?
What would the decision be if the sample mean had been 104 N?
BONUS QUESTION:
If the true mean breaking load of the new wires is 106.0 N, then what is the probability that another random sample of 36 wires, with the same sample standard deviation, will lead to an incorrect decision?
What type of error is the event in part (e)?
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