An alien empire is considering taking over planet Earth, but they will only do so if the portion of rebellious humans is less than 10%.

1. An alien empire is considering taking over planet Earth, but they will only do so if the portion of rebellious humans is less than 10%. They abducted a random sample of 400 humans, performed special psychological tests, and found that 14%  of the sample are rebellious. Perform a hypothesis test at a significance level of , to test the claim that more than 10% of humans are rebellious.

2. Suppose we measured the IQ scores of the 42 students in NURS561, and calculated a mean IQ score of 108.2, and a standard deviation of 6.27. If we make no assumptions about the population mean and standard deviation of IQ scores, test the hypothesis that students in NURS561 have a mean IQ greater than 100. Use a significance level of .