STA 2023 Homework 3 Deadline: 3/29/2015 in class Name: Only paper version will be graded. Any submission after deadline will not be graded unless with sufcient document. Problem 1(30 points) Assume the age of all students in FSU have standard deviation 5. We randomly choose 100 students as our sample and get the average age of our sample is 19. (hint: use z*) I. What is the point estimate of the average age of all FSU students? (10') II. What is the condence interval estimate of the average age of all FSU students with condence level 90%? (10') III. What is the condence interval estimate of the average age of all FSU students with condence level 95%? (10') Page 1 of 3 Problem 2(30 points) We would like to know the average age of FSU students. But due to the limit funding, we can only recruit for participants. Their age are: 19, 24, 28, 37. Now we can only estimate based on our four samples: there is no information about population in this question. (hint: use t*) I. What is sample average and sample standard deviation?(10') II. What is the condence interval estimate of the average age of all FSU graduate students with condence level 90%?(10') III. What is the condence interval estimate of the average age of all FSU graduate students with condence level 95%?(10') Page 2 of 3 Problem 3(40 points) Assume IQs of all people have mean 100 and standard deviation 15 (notice here the IQ is not necessarily Normal Distributed). I. Write out what is the Central Limit Theorem. (10')(Hint: what is the distribution of sample average? including the name of distribution and its parameter) II. We randomly choose 40 people as our sample, then what is the sampling distribution of average IQ of our sample? (10') III. What is the probability that the average IQ of our sample higher than 105? (10') IV. What is the probability that the average IQ of our sample lower than 95? (10') Page 3 of 3