For each question below you will run a hypothesis test. Use alpha=.05 for all tests. Show all steps including what the null and alternative hypotheses are, what the test statistic is, what the critical value (or p-value) is, what you can conclude in full sentences in terms of the given situation.

1) A principal at a specific school thinks that his students are above average intelligence. He collects a random sample of IQ scores from 25 students from his school. His sample has a mean of 112. The mean population IQ is 100 with a standard deviation of 15. Does he have enough evidence to support his claim?

2) A simple random sample of 14 people from a certain population gives body mass indices as shown in the Table below. Can we conclude that the mean BMI for this population is different from 35? Explain.

Subject BMI 23 2 25 3 21 4 37 U 39 O 21 7 23 24 9 32 10 57 11 23 12 26 13 31 14 45