The quality control manager at a lightbulb factory needs to determine whether the mean life of a large shipment of lightbulbs is equal to 375 hours. The population standard deviation is 100 hours. A random sample of 20 lightbulbs indicates a sample mean life of 350 hours. (a) State the appropriate null and alternative hypotheses. (b) At the 0.05 level of significance is there evidence that the mean life is smaller than 375 hours? (c) Describe the Type I error and Typer II errors in the context of the setup in part (a)