in 2010, the Maricopa Community College District's enrollment data showed the following breakdown of students by ethnicity: 54.9% White; 21.1% Hispanic; 7.9% Black; 4.5% Asian/Pacific Islander; 2.9% Native American; 8.8% Other. Information was collected from a random sample 0f 300 students in 2017 to determine whether or not the data has changed significantly. The sample data is given in the table below. At the  α=0.05 level of significance, test the claim that the ethnic breakdown of students at MCCCD has not changed significantly since 2010.

Which would be correct hypotheses for this test?

• H0:The breakdown of students by ethnicity has changed significantly since 2010 (i.e. the given distribution no longer fits); H1:The breakdwon of students by ethnicity has not changed significantly since 2010 (i.e. the given distribution still fits)
• H0:The breakdown of students by ethnicity has not changed significantly since 2010 (i.e. the given distribution still fits);  H1:The breakdown of students by ethnicity has changed significantly since 2010 (i.e. the given distribution no longer fits)
• H0:μ1=μ2;H1:μ1≠μ2
• H0:p1=p2;2H1:p1≠p2

Ethnicity of students in sample:

Test Statistic:



Give the P-value:



Which is the correct result:

• Do not Reject the Null Hypothesis
• Reject the Null Hypothesis

Which would be the appropriate conclusion?

• There is enough evidence to suggest that the breakdown of students by ethnicity has changed significantly since 2010.
• There is not enough evidence to suggest that the breakdown of students by ethnicity has changed significantly since 2010.

Hydraulics & Hydrology

Problem Statement

The Romans were exquisite water engineers, and that without having at their disposal the modern tools and the knowledge we have today. Remember that Hydraulics and Hydrology as we know it now only came to be in the 1700’ when engineers started to put a fundamental framework together that is/was based on lab experiments and theoretical approaches and principles. Until then, you just “knew”. The Romans build all sorts of hydraulic systems, from irrigation canals, to water supply infrastructure, to the famed “hot baths” of Rome, to sewer systems, you name it. They realized that if you want water for different purposes at locations that were important to you that very often you had to get the water there because it just was not available in close proximity.

One of the marvelous feats they accomplished was to build water supply systems that would run over dozens of miles to convey water from sources to locations of need, typically the towns and cities they founded in their vast empire. They managed to do so by building a lot of infrastructure that withstood time and that, almost 2000 years later, is still in place for us to marvel at. Especially the many bridges that were built to cross valleys and gorges to keep the supply line flowing as an open channel are spectacular in their construction, such as the Pont du Gard, Segovia, and Aquila aqueducts.

Task:

1. Create a small inventory of the 5 most prominent and well-known aqueducts around to this day (you make a decision on what the criteria are for the selection of the 5). Come up with some describing parameters (for sure show an image or two) such as location, total length, capacity, year of built, special features, how many bridges, building materials, etc. Be creative and decide on your own what you want to tell about them.

2. Pick one of them and carry out a hydraulic analysis. I am interested here in typical characteristics such as discharge capacity, slopes, cross sections, but also operation: how did you get the water into the aqueduct, control structures, terminal end structures, Manning’s “n”, ... But also how they were lined, how gaps between construction elements were sealed so no seepage (or losses) would occur. It would also be great if you could treat the aqueduct as a chain of: uniform, rapidly (around controls), and gradually varied flow sections. Carry out a few analyses steps and report on what happens to energy and friction grade lines in these sections, preferably of the entire length of the aqueduct.

Suppose I did a poll of my students in my Economics courses. I asked each student to rate himself/herself relative to the other students in class. I then found 90% of students rated themselves above average. What type of bias is relevant here?

From the first test, 65% of the class received an ‘A’ grade.

1. Sampling 5 students, what is the probability that 1 will have an A?

2. Sampling 6 students, what is the probability that all 6 will have an A?

3. Sampling 12 students, what is the probability that at LEAST 9 will have an A?

the results of a special exam are shown below. can the teacher conclude that the even ing students have a higher score? use alpha=.01.

day students.                   eve students
n=36.                                  n=41
mean = 69.                          mean = 72
s= 5.8.                                 s= 6.3

Suppose the heights of students are normally distributed with mean 172 and variance 9.

a) Randomly pick two students. What's the probability that the first student is taller than the second student?

b) Randomly pick two students. What's the probability their average height is larger than 175?

a simple random sample of 225 college students was taken in order to estimate the proportion of college students that agrees with the "no teacher left alone act". of those surveyed, 142 agreed with the law. construct the 95% confidence interval estimate of the proportion of all college students that agrees with this law

Here we consider the sleep habits of med students versus non-med students. The study consists of the hours of sleep per day obtained from 27 med students and 30 non-med students. The summarized data is given in the table. Here, x¯x¯ is the mean hours of sleep per day from each sample. The degrees of freedom (d.f.) that you must use in your calculations are given below.

Test the claim that the mean hours of sleep for med and non-med students is different. Use a 0.05 significance level.

(a) Find the test statistic.

(b) Find the P-value.

(c) Is there sufficient data to support the claim?
Yes
No

Test the claim that, on average, med students get less sleep than non-med students. Use a 0.05 significance level.

(d) Is there sufficient data to support the claim?
Yes
No

Q1. A local sports bar wanted to determine whether Ohio University students prefer a particular type of food in their establishment. A sample of students responses are reproduced below. Do students prefer a particular type of bar food? Use critical value = 6.58.

Use the numbers below for this question only!

Nachos        Pizza        Chicken Wings        Cheese Sticks

   33               34                    46                          46


What would the expected value for Cheese Sticks be?

Q2. A local sports bar wanted to determine whether Ohio University students prefer a particular type of food in their establishment. A sample of students responses are reproduced below. Do students prefer a particular type of bar food? Use critical value = 6.58.

Use the numbers below for this question only!

Nachos        Pizza        Chicken Wings        Cheese Sticks

   44               40                    42                          43


What is the calculated chi-squared value?

Q.3 Using a critical value of 6.58, was there a significant preference for what students eat in a sports bar based on the obtained chi-square value in Question 2?

Yes

No

Question Four

An academic conference held this past January consistent of 250 participants including undergraduate students, masters students, PhD students, and, professors from business faculties, engineering faculties, and nursing faculties to discuss various ways of increasing the learning desires of students. The following table gives us the breakdown of participants by levels of education and faculties.

                                                                Business               Engineering               Nursing                    Totals

Undergraduate students                     30                               15                               35                               80

Masters students                                    40                               38                               12                               90

PhD students                                             10                               12                               8                               30

Professors                                                  20                               15                               15                               50

Totals                                                        100                               80                               70                           250

1. The probability that this participant is from business is __ 100/250_____

2. The probability that this participant is a PhD student is __30/250____

3. The probability that this participant is a nursing professor is __15/50_____

4. The probability that this participant is either an undergraduate or a master’s student is _170/250_______

5. The probability that this participant is either from business or a PhD student is ________

6. The probability that this participant is a Professor knowing that he/she is in nursing is ________

7. The probability that this participant is from business knowing that he/she is a master’s student is

_____