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A supervisor at a manufacturing facility claims that the automated/robotic machinery they recently purchased is overfilling one of their products (which has an advertised = 100 gram label on the packaging). If a sample of size 45 selected from this population reveals a sample mean of 103.4 grams, test the hypothesis that > 100 at a 1% level of significance by completing the following steps. Assume that is known to be 6.5 grams.

a) State the null and alternative hypotheses.

b) Determine the critical and calculated values of Z.

c) Decide whether to reject the null hypothesis and state your conclusion