1. A university planner is interested in determining the percentage of spring semester students who will attend summer school. She takes a pilot sample of 160 spring semester students discovering that 56 will return to summer school.
   
   1. Construct a 90% confidence interval estimate for the percentage of spring semester students who will return to summer school.
   2. Construct a 95% confidence interval estimate for the percentage of spring semester students who will return to summer school.

Part I - Do Students Really Cheat? (30%)

In a recent poll 400 students were asked about their experiences with witnessing academic dishonesty among their classmates. Suppose 172 students admitted to witnessing academic dishonesty, 205 stated they did not and 23 had no opinion. Use the sign test and a significance of 0.05 to determine whether there is a difference between the number of students that have witnessed academic dishonesty compared to those that have not.

Suppose the heights (in inches) of all college students follow a Normal distribution with standard deviation σ=3. A sample of 25 students is taken from the population; the average height of these students is 68.4 inches. Does this sample data provide strong evidence that the average height of all students is less than 70 inches?

Which test should be used?

What is the null hypothesis?

What is the alternative hypothesis?

What is the p-value?

The council of higher education wants to compare the percentage of students that score A in two universities. In a random sample of 50 students from university one, 16 received a grade of A; and in a random sample of 40 students from university two, 8 received a grade of A. The 95% confidence interval for the difference in the proportion of students who received a grade of A is:

a. -0.0638 to 0.3038

b. -0.0691 to 0.2983

c. 0.0365 to 0.04302

d. -0.0591 to 0.2991

1. One of the student recruiters at UCW has surveyed 160 students regarding their interest to stay in Canada after graduation. 135 of the students stated that they would like to stay in Canada.

1. Construct the 95% confidence interval about the true proportion of all of the UCW students who would consider staying in Canada after graduation.

2. Calculate how many students he should survey to have the result with less than 0.05 error.

Refer to the following contingency chart comparing 3 college programs (criminal justice, business, culinary) with the GPA of students graduating from those programs at a college.

                                            2.0-2.5            2.5-3.0            3.0-3.5               3.5-4.0

criminal justice                     23                    18                     32                       47

business                               17                     26                    36                        31

culinary                                 28                     17                    41                       28

A. What is the overall total number of students in this contingency table?

B. What is the observed value for business students with a GPA of 3.0-3.5?

C. What is the expected value for criminal justice students with a GPA of 2.0-2.5?

D. The total number of students with a GPA 2.5-3.0 is?

E. What is the total number of culinary students?

F. What is the value for (O-E)²/E value for the criminal justice students with a GPA of 2.0-2.5?

G. What is the value of the test statistic?

H. Assuming α = 2.5%, the critical value is ?

I. Assuming α = 2.5%, what is the conclusion to this independence test?

1. Suppose that a large public university is experiencing a budget shortfall. They decide to increase tuition to try to make up for the difference. Last year (2017) the school charged out-of-state tuition of $18,000 and instate tuition of $8,000. The enrollment numbers for 2017 were 5,000 out-of-state students and 12,000 instate students. During the 2018 academic year tuition for out-of-state students increased to $20,000, and for in-state it increased to $9,000. The enrollment for 2018 dropped to 4,000 out-of-state and 11,000 instate students. a. (3 points) Calculate the price elasticity of demand for out-of-state students. Then calculate the price elasticity of demand for in-state students. (Round to 3 decimal places).

b. (2 points) Based on part a, how would you characterize demand for each group of students? Explain whether these results are what you would predict for this situation.

c. (2 point) Did this university make the right decision by raising each tuition rate? How could the administration use this information to maximize revenue?

There are 180 primary schools in a country area having an average of 30 or more people under the age of 21 per class. A sample of 30 schools drawn using systematic sampling with an interval of k = 6.

1. Estimate total number of students.
2. Estimate average number of students per farm.
3. The variance of the sample mean of students per farm.
4. 95% confidence interval for the total number of students.

Question 1:

There are 180 primary schools in a country area having an average of 30 or more people under the age of 21 per class. A sample of 30 schools drawn using systematic sampling with an interval of k = 6.

1. Estimate total number of students.
2. Estimate average number of students per farm.
3. The variance of the sample mean of students per farm.
4. 95% confidence interval for the total number of students.