Discuss the below problems:
Q1: The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude, and study habits of college students. Scores range from 0 to 200 and follow (approximately) a normal distribution with mean 115 and standard deviation 25. You suspect that incoming freshmen have a mean u which is different from 115 because they are often excited yet anxious about entering college. To test your suspicion, you test the hypothesis
H0: u = 115
Ha: u not equal 115
You give the SSHA to 25 students who are incoming freshmen and find their mean score is 116.2. Assuming that the scores of all incoming freshmen are approximately normal with the same standard deviation as the scores of all college students, the P-value of your test would be?
Q2: The level of calcium in the blood of health young adults follows a normal distribution with mean u = 10 milligrams per deciliter and standard deviation 0.4. A clinic measures the blood calcium of 25 health pregnant young women at their first visit for prenatal care. The mean of these 25 measurements is xbar = 9.6. Is this evidence that the mean calcium level in the population from which these women come is less than 10? To answer this, test the hypothesis:
H0: u = 10
Ha: u < 10
The P-Value of this test would be?