Question: [10 points] A lumber manufacturer supplies pressure treated lumber to a local hardware store in 8ft pieces. Due to machine imperfections, there is a little variability in the length of the pieces. Some are a little shorter, others a little longer, than 8ft. A standard deviation of no more than 0.5inches is considered acceptable. The lumber supplied in the past has been within specs, but since it has not checked in a while, the hardware store decided to test if supplies are not meeting specs. It randomly selected 45 pieces of lumber and check their lengths. A sample mean of 8ft and a sample standard deviation of 0.6inches was obtained. At a 5% significance level, conduct the appropriate hypothesis test and determine if the lumber supplied fails to meet specs.

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