Sally has now graduated and become director of quality control for a major cookie conglomerate. The company uses an average of 2000 chocolate chips per batch of cookies, with a known standard deviation of 42 chips.

a) Sally wishes to test the hypothesis that µ=2000 chips per batch against the alternative that µ is different from 2000. She conducts a random sample of 50 batches and finds a mean of 1988 chips. What test statistic will be used, and what is its value?

b) Find the P-value and interpret your answer from part (a): for what α is the mean significantly different from 2000?

c) Find a 95% confidence interval for µ and compare your results with your conclusions above.