#4
**Below are two samples of test scores from two different calculus classes. It is believed that class 1 performed better than class two. From previous tests, it is known that the test scores for both classes are normally distributed and the population standard deviation of class 1 is 10 points and the population standard deviation of class 2 is 8 points. Do the data support that class 1 performed better.**
```{r}
class1<-c(100, 86, 98, 72, 66, 95, 93, 82)
class2<-c(98, 82, 99, 99, 70, 71, 94, 79)

```

##5
**A teaching assistant in Florida collected a sample to see if the average number of hours students put into studying depending on if they were in graduate school or not. The data below represents these two samples.**

**Perform a test to determine if the time graduate students spend studying is greater than that of undergraduate students. Be sure to identify your hypotheses and explain your conclusion in the context of the question. Assume the time spend studying for both graduate and undergraduate is normally distributed.**

grad<-c(15,7,15,10,5,5,2,3,12,16,15,37,8,14,10,18,3,25,15,5,5)
undergrad<-c(6,8,15,6,5,14,10,10,12,5)

Please Solve using R studio codes with explanation

A teacher instituted a new reading program at school. After 10 weeks in the​ program, it was found that the mean reading speed of a random sample of 20 second grade students was

94.4 wpm. What might you conclude based on this​ result? Select the correct choice below and fill in the answer boxes within your choice.

​(Type integers or decimals rounded to four decimal places as​ needed.)

A. A mean reading rate of 94.4 wpm is not unusual since the probability of obtaining a result of 94.4 wpm or more is ____. This means that we would expect a mean reading rate of 94.4

or higher from a population whose mean reading rate is 92 in ____ of every 100 random samples of size n=20 students. The new program is not abundantly more effective than the old program.

B. A mean reading rate of 94.4 wpm is unusual since the probability of obtaining a result of 94.4 wpm or more is ____. This means that we would expect a mean reading rate of 94.4

or higher from a population whose mean reading rate is 92 in ____ of every 100 random samples of size n=20 students. The new program is abundantly more effective than the old program.

During the last couple of decades, colleges and universities have tried to increase their number of minority students by various forms of affirmative action. At Campus X, this has led to no small amount of dissension. Some students complain that the policy of accepting students with lower SAT and other scores just because of their race or minority status is unfair. Others believe that the diversity that results from such policies is good for everyone because we should learn to live together and a university campus should be a place to do this. Still, there is some question, even among members of this group, as to how well the integration is working. Furthermore, a different type of problem has recently surfaced. Because Asian Americans were represented in numbers grater than their percentage of the population, some universities were restricting the percentage of the population they would accept even when their scores were higher than others they did accept. Also, in some cases where affirmative action has been eliminated, the number of minority members accepted into certain medical and law schools has plummeted, and many people find this alarming.

Do you think that diversity ought to be a goal of campus admissions?

Or do you believe that only academic qualifications ought to count? Why?

Let us say that the SBRU information system includes four subsystems: Resort relations, Student booking, Accounting and finance, and Social networking. The first three are purely Web applications, so access to those will be through an Internet connection to a Web server at the SBRU home office. The Social networking subsystem has built-in chat capabilities. It relies on Internet access for the students, as students compare notes before they book their travel reservations and as they chat while traveling. To function properly, the system obviously requires a wireless network at each resort during the trip. SBRU isn’t responsible for installing or maintaining the resort wireless network; they only plan to provide some design specifications and guidelines to each resort. The resort will be responsible for connecting to the Internet and for providing a secure wireless environment for the students.

1. Design the environment for the SBRU information system by drawing a network diagram. Include what might be necessary to support online chatting capabilities.

2. Considering that everything is designed to operate through the Internet with browsers or smart phones, how simple does this architecture appear to be? Can you see why Web and smart phone applications are so appealing?

3. What aspect of design becomes extremely important to protect the integrity of the system?

You are the director of an admission office. Your job every year is to decide the number of offer letters to issue to undergraduate degree applicants. For the academic year 2016/2017, the university has a capacity to enroll 7,200 undergraduate students, but you received more than 20,000 applications. However, you know from past year records many students also got offers from other good schools in Canada and the US. The yield rate for this university is far less than 100%.

Assume the university has spent large amount of sunk cost in its undergraduate program for a designed capacity to enroll 7,200 students, such as upgrading classrooms, expanding residential houses, hiring additional teaching instructors and administration staff. As the admission office director, you need to consider following questions:

(a) Will you issue more than 7,200 offer letters for 2016/2017 academic year?

(b) What is the trade-off between issuing more than 7,200 offer letters and issuing exactly 7,200 offer letters?

(c) How to determine the optimal number of offer letters to issue? What information do you need, and how to get such information?

Complete the reading of NIST Special Publication 800-145 (2011). NIST Definition of Cloud Computing, then branch out into Internet research on how the term “Cloud Computing” has evolved and what it means now. You can talk about how cloud services are increasingly relevant to businesses today. Feel free to use an example for Infrastructure as a Service (IaaS) or Software as a Service (Saas) and talk about why companies are moving their onsite infrastructure to the cloud in many cases. Think Microsoft Azure, Amazon Web Services, Rackspace, or any number of cloud providers.

Go ahead and have a little fun with it if you like also: Pretend you are an IT manager and need to recommend a solution for moving a piece of software or hardware into the cloud. What provider would you use and why? Or would you instead recommend keeping servers/software in house?

You must post your initial response (with APA 6th ed or higher references) before being able to review other students' responses. Once you have made your first response, you will be able to reply to other students’ posts. You are expected to make a minimum of 3 responses to your fellow students' posts.

A)While testing a building's fire alarms, the probability that any fire alarm will fail is 0.01. Suppose a building has 10 fire alarms, all which are independent of one another. The test will be passed if all fire alarms work.

a) 5 buildings are tested on the same day and each building has 10 fire alarms. How likely is it that 4 or more buildings pass the test? ( A building will pass if all 10 fire alarms are good)

B) Customers arrive at a restaurant according to a Poisson process at a rate of 30 customers per hour. There is a probability of 0.8 that a customer will dine in.

b) Say the customers are arriving independently of one another. What is the probability that 30 customers will arrive in a 1 hour time period AND all 30 will dine in?

C) Suppose a phd applicant is either accepted to a graduate program or not. if accepted the student can choose to attend or not attend. Suppose a graduate program has sent acceptance letters to 50 applicatns, but only had enough funding for 30 students. Let the students who were accepted to the program be independent of one another and the chance that a student will join the program be 0.6.

c) what is the probability that the graduate program will have enough funding for all students that joins the program.

Now provide confidence interval information from the previous question. Specifically:

a.    What is the value of the point estimate of the difference between the two population proportions?

b.    What is the margin of error at 90% confidence?

        (± what value; please provide to 4 decimals; e.g. "0.1234")

c.    With that margin of error, what is the low number in the confidence interval?

d.    With that margin of error, what is the high number in the confidence interval?

Formatting your answer; your answer, typed in, should look something like this:

a.    .05

b.    .1234

c.    -.0734

d.    .1734

5(a)What is the probability that out of 200 pieces of randomly selected glass, more than fifty-five of them are defective. [5 marks]

A sample of 12 of bags of Calbie Chips were weighed (to the nearest gram), and listed here as follows.

219, 226, 217, 224, 223, 216, 221, 228, 215, 229, 225, 229 Find a 95% confidence interval for the mean mass of bags of Calbie Chips.

[9 marks]

(b) Professor GeniusAtCalculus has two lecture sections (A and B) of the same 4th year Advanced Calculus (AMA 4301) course in Semester 2. She wants to investigate whether section A students maybe ”smarter” than section B students by comparing their perfor- mances in the midterm test. A random sample of 12 students were taken from section A, with mean midterm test score of 78.8 and standard deviation 8.5; and a random sample of 9 students were taken from section B, with mean midterm test score of 86 and standard deviation 9.3. Assume the population standard deviations of midterm test scores for both sections are the same. Construct the 90% confidence interval for the difference in midterm test scores of the two sections. Based on the sample midterm test scores from the two sections, can Professor GeniusAtCalculus conclude that there is any evidence that one section of students are ”smarter” than the other section? Justify your conclusions.

[8 marks]

(c) The COVID-19 (coronavirus) mortality rate of a country is defined as the ratio of the number of deaths due to COVID-19 divided by the number of (confirmed) cases of COVID-19 in that country. Suppose we want to investigate if there is any difference between the COVID-19 mortality rate in the US and the UK. On April 18, 2020, out of a sample of 671,493 cases of COVID-19 in the US, there was 33,288 deaths; and out of a sample of 109,754 cases of COVID-19 in the UK, there was 14,606 deaths. What is the 92% confidence interval in the true difference in the mortality rates between the two countries? What can you conclude about the difference in the mortality rates between the US and the UK? Justify your conclusions. [8 marks]

Do students reduce study time in classes where they achieve a higher midterm score? In a Journal of Economic Education article (Winter 2005), Gregory Krohn and Catherine O’Connor studied student effort and performance in a class over a semester. In an intermediate macroeconomics course, they found that “students respond to higher midterm scores by reducing the number of hours they subsequently allocate to studying for the course.” Suppose that a random sample of n = 8 students who performed well on the midterm exam was taken and weekly study times before and after the exam were compared. The resulting data are given in Table 10.6. Assume that the population of all possible paired differences is normally distributed.

Table 10.6

Paired T-Test and CI: Study Before, Study After

95% CI for mean difference: (5.20929, 10.79071)

T-Test of mean difference = 0 (vs not = 0): T-Value = 6.78, P-Value = .0003

(a) Set up the null and alternative hypotheses to test whether there is a difference in the true mean study time before and after the midterm exam.

H₀: µ_d =  versus H_a: µ_d ≠

(b) Above we present the MINITAB output for the paired differences test. Use the output and critical values to test the hypotheses at the .10, .05, and .01 level of significance. Has the true mean study time changed? (Round your answer to 2 decimal places.)

t =   We have (Click to select)strongvery strongextremely strongno evidence.

(c) Use the p-value to test the hypotheses at the .10, .05, and .01 level of significance. How much evidence is there against the null hypothesis?

There is (Click to select)extermly strong evidenceno evidencestrong evidencevery strong evidence against the null hypothesis.