1. Benzene is a toxic chemical used in the manufacturing of medicinal chemicals, dyes, artificial leather, and linoleum. A manufacturer claims that its exit water meets the federal regulation with a mean of less than 7980 ppm of benzene. To assess the benzene content of the exit water, 10 independent water samples were collected and found to have an average of 7906 ppm of benzene. Assume a known standard deviation of 80 ppm and use a significance level of 0.05.

1.1. (2 points) What is the -value if the true mean is 7950?

1.2. (2 points) What sample size would be necessary to detect a true mean of 7950 with a probability of at least 0.99?