Question: Consider the following problem, State the null and alternative hypotheses. Determine which distribution to use for the test statistic. Calculate the test statistic. Draw a conclusion based on your findings.

A manufacturer must test that his bolts are 2.00 cm long when they come off the assembly line. He must recalibrate his machines if the bolts are too long or too short. After sampling 100 randomly selected bolts off the assembly line, he calculates the sample mean to be 1.90 cm. He knows that the population standard deviation is 0.50 cm. Assuming a level of significance of a = 0.05, Is there sufficient evidence to show that the manufacturer needs to recalibrate his machines?

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