Solve these questions

QUESTION I: (5 marks) [Hint: For the following questions. you may use the Z score table provided in the appendix.] i. A principal at a certain school claims that the students in his school have above average intelligence. The mean 1Q score of 30 randomly sampled students is 1 12.5. The mean IQ score of the population is 100 with the standard deviation of 15. Show whether there is sufficient evidence to support the principal's claim? [Hint: Use a = 0.05] [2.5 marks] li. Suppose the courage score of psychologists has a population that is normally distributed with a standard deviation of 10, when measured through the aptitude test. You decide to sample 57 psychologists from this population and obtained a mean score of 34.8 1 and a standard deviation of 9.0579. Using the value of a = 0.05. determine whether the observed mean is significantly greater than an expected courage score of 34? [2.5 marks]