A study of 100 students in a local university gave the average GPA to be 3.1 with a standard deviation of.5. The same study revealed that in this sample, 20% are out of state students.

1. The lower bound, correct up to 3 decimal places for a 92% confidence interval for the actual GPA of students in this university is

2. The lower bound, correct up to 3 decimal places of a 90% confidence interval for the true proportion of out of state students is

3. The lower bound, correct up to 3 decimal places, of a 95% confidence interval for the true GPA with a sample size of 20, a sample mean of 3.1 ad a standard deviation of 0.5 is

4. The exact number of students that need be surveyed for the true GPA to be estimated within .5 units with a 96% confidence

Imagine Penn State were to hold summer events for High school students. Should it include freshman and sophomores? Or be open to all high school students & their families titled "College 101." What should Penn State do? What do families and students need to know at that point in their highschool to start considering? Who should they listen to? What do you wish you would have known then to help set you up for success? Would a panel discussion be helpful? If so, what panels? College admissions essay reviewers? College students? What should they see? Is there anything they should know about why you chose Penn State? Since it's high school and most of the students would be local, what are some selling points?

56 randomly selected male students at a commuter college were asked if they lived with their parents. 24 responded yes.   51 randomly selected female students at the same college were asked if they lived with their parents. 21 responded yes. The Dean of Students believes that more male students than female students live independently of their parents. Test the dean’s assumption. Use α=.05

1. Pooled sample proportion & compute the test statistic (Population 1 is Males, Population 2 is females)

     where

2. Critical value method, then draw the graph and mark the critical region and the test statistic.

3. P-value method, then compute the area to the right of the test statistic to get the P-value =

4. Compare to α=.05 and make a decision to reject or fail to reject the null hypothesis.

An article was released claiming that undergraduate SHU students study a mean of 250 hours per semester. You want to gather data to prove that the mean study time per semester for undergraduate SHU students is actually more than 250 hours. You take a sample of undergraduate SHU students and find their mean study time to be 265 hours per semester with a standard deviation of 70 hours. Answer the following questions using α = .1.

1. State the null and alternative hypotheses. (3 pts)

2. State the rejection rule, find the test statistic, and conclude whether or not you reject the null hypothesis (and with how much confidence)

if: (a) the sample consisted of 25 students. (9 pts) (b) the sample consisted of 100 students. (8 pts)

A study of undergraduate computer science students examined changes in major after the first year. The study examined the fates of 256 students who enrolled as first-year students in the same fall semester. The students were classified according to gender and their declared major at the beginning of the second year. For convenience we use the labels CS for computer science majors, EO for engineering and other science majors, and O for other majors. The explanatory variables included several high school grade summaries coded as 10 = A, 9 = A-, etc. Here are the mean high school mathematics grades for these students.

Describe the main effects and interaction using appropriate graphs and calculations.

The distribution of statistics marks of some sandwich students was found to be normal with a mean within a range of 61- 65 and a standard deviation of within a range of 7.8 – 8.6 (1dp). It was found out that there were 348 students who took the course. With an assumed mean and standard deviation, answer the questions that follow: a. If the minimum mark to qualify for an interview was 43. What is the probability that a student selected at random qualified for the interview and what percentage did not qualify? (5marks) b. If the cut-off mark for selection is 48, how many and what percentage of the students were selected? c. How many students scored a mark greater than 54 but less than 78? d. How many students from the group scored a mark greater than 68 but less than 80?

MAT 240 Applications of Two-Sample Tests

I asked half of my students how often they exercise each week.

Population 1 (My students) Sample Size: 10

Population 1 Student Responses: 0, 0, 2, 3, 5, 5, 5, 5, 5, 6

For the second population, I asked students in the classroom next door (which has kids that are 3 years older than my students) the same question.

Population 2 (Classroom next door): Sample Size: 10

Population 2 Student Responses: 2, 3, 3, 4, 4, 5, 5, 5, 6, 7

I hypothesize that students in older classrooms exercise more. Test my hypothesis at a .05 significance level.

11. (20) GPA distribution in UPW university is a normal distribution with an average of 2.68 and a standard deviation of 0.4.

(a) About what proportion of the students have GPA at most 3?

(b) About what proportion of the students’ GPA are between 2 and 3?

(c) The President of the university is establishing a new scholarship, the minimum qualification is that students GPA have to be among top 3%, what is the numerical GPA a student must have in order to qualify?

(d) A students’ club has a minimum GPA requirement of 2.7 or higher. You heard that Kelly is going to attend a club members’ meeting, you are wondering: what is the chance that Kelly’s GPA is lower than 3.3?

(e) If we randomly choose 7 students in the university, what is the chance that at least 2 have GPA over 3.3?

Three Finance majors have differing opinions about AAPL stock, which currently trades
at $300/share. Finance student 1 is very bullish and decides to purchase
shares of AAPL on margin. Student 2 feels the opposite and uses margin to sell short the same
number of shares of AAPL. Student 3 isn’t sure but feels AAPL will be volatile over the next year
and buys an ATM straddle. One year from today, AAPL trades at exactly $300/share. Which
student(s), if any, will see a negative ROI on their investment strategy, under normal
assumptions of transaction costs.

Student 2

All 3 students

None of the Students

Students 1 and 2

Students 2 and 3

Student 3

Student 1

Students 1 and 3

11. (20) GPA distribution in UPW university is a normal distribution with an average of 2.68 and a standard deviation of 0.4.

(a) About what proportion of the students have GPA at most 3?

(b) About what proportion of the students’ GPA are between 2 and 3?

(c) The President of the university is establishing a new scholarship, the minimum qualification is that students GPA have to be among top 3%, what is the numerical GPA a student must have in order to qualify?

(d) A students’ club has a minimum GPA requirement of 2.7 or higher. You heard that Kelly is going to attend a club members’ meeting, you are wondering: what is the chance that Kelly’s GPA is lower than 3.3?

(e) If we randomly choose 7 students in the university, what is the chance that at least 2 have GPA over 3.3?