Two random samples are taken, one from among UVA students and the other from among UNC students. Both groups are asked if academics are their top priority. A summary of the sample sizes and proportions of each group answering yes'' are given below:

UVA (Pop. 1):UNC (Pop. 2):n1=85,n2=100,p̂ 1=0.733p̂ 2=0.635UVA (Pop. 1):n1=85,p^1=0.733UNC (Pop. 2):n2=100,p^2=0.635

Find a 95.4% confidence interval for the difference p1−p2p1−p2 of the population proportions.

6. Last year it was found that on average it took students 20 minutes to fill out the forms required for graduation. This year the department has changed the form and asked graduating student to report how much time it took them to complete the forms. Of the students 22 replied with their time, the average time that they reported was 18.5 minutes, and the sample standard deviation was 5.2. Can we conclude that the new forms take less time to complete than the older forms? Use a 0.1 significance level (i.e., p-value). (Assume that the reported times follow a Gaussian distribution)

Enrollment Management. An engineering department chair wants to maximize the use of scholarship dollars to shape the enrollment of the incoming freshmen. All applicants take an engineering aptitude test and receive a scholarship based on their score. Here is the scholarship award amount:

The department chair wants to

award scholarships to 100 students

with at least 5 scholarships given to students in each test score

and a total of $350,000 spent on the 100 scholarships.

What is the maximum average test score the freshmen class can have?

Question
(a) Consider a random sample of the following data: 254, 261, 250, 258, 253, 257.
Calculate the unbiased estimator of the population variance.

(b) Suppose the GPA of all students enrolled in a particular course can be modelled by a
certain distribution with a mean of 3.4 and variance 0.3. Compute the probability that the
mean GPA of a random sample of 40 students selected from this course will be:

(i) lower than 3.2
(ii) between 3.3 and 3.6

(c) Suppose you throw a die 600 times. Apply a suitable technique to compute the
approximate probability of obtaining between 90 and 110 fours.

Descriptive analysis revealed that the mean Test 3 score of all 63 students in Dr. Bills’s statistics courses was an 80. Similarly, the standard deviation for all students’ Test 3 scores was found to be 16. Assume the Test 3 scores are approximately normally distributed.

5. Determine the Test 3 score that corresponds to a z-score of -2.18. Round your solution to the nearest whole number.

6. Find the 75^th percentile. That is, find the test score such that 75% of all test scores are below it. Hint: See example on the Chapter 6 handout. Round your solution to the nearest whole number.

A random sample of 12 second-year university students enrolled in a business statistics course was drawn. At the course’s completion, each student was asked how many hours he or she spent doing homework in statistics. The data are listed here. It is know that the population standard deviation is 8. The instructor has recommended that the students devote 36 hours to the course for the semester. Test to determine at the 1% significance level whether there is evidence that the average student spent less than the recommended amount of time. 31 40 26 30 36 38 29 40 38 30 35 38

Question 3: Show the following verbal expressions (a,b,c,d) for two different sets with the appropriate mathematical symbols and definitions for two different sets of definitions.(predicate logic)
It is assumed that the first set of definitions is students in the class and the second set of definitions is all people. How could we express e option using propositional logic?

a) Some of the students in the class can speak German.
b) Everyone in the class is friendly.
c) There are those who are not born in California in the classroom.
d) A student from the class went to the theater.
e) Nobody in the classroom knows object-oriented programming.

College students were asked to rate the spring festivals at university in years 2016, 2017, and 2018. The following table shows the students’ ratings on a scale from 0 to 100 where larger values are assigned to better activities. Construct an ANOVA table and determine whether there is a significant difference among the student appreciation of spring festivals for different years. Assume a significance level of α = 0.05.

2.Thirty GPAs from a randomly selected sample of statistics students at a college are linked below. Assume that the population distribution is approximately Normal. The technician in charge of records claimed that the population mean GPA for the whole college is 2.81. a. What is the sample​ mean? Is it higher or lower than the population mean of 2.81​? b. The chair of the mathematics department claims that statistics students typically have higher GPAs than the typical college student. Use the​ four-step procedure and the data provided to test this claim. Use a significance level of 0.05.

2.86,3.37,3.17,2.51,3.49, 2.75, 3.04, 3.59,2.65,3.97,2.89,2.66,3.52,3.06, 2.79,3.45,2.47,3.14,3.43,3.13,3.18,3.08,3.09,2.96,3.49, 3.43,2.73,3.14, 3.11,3.03

Two different teaching procedures were used on two different groups of students. Each group contained 100 students of about the same ability. At the end of the term, an evaluating team assigned a letter grade to each student. The results were tabulated as follows:

Grade Group

A B C D F Total

Total (I) 15 22 32 17 14 100

(II) 9 16 29 28 18 100

If we consider this data to be comprised of independent observations, test at the 5 percent significance level the hypothesis that the two teaching procedures are equally effective.