At UC San Diego, incoming students are each randomly assigned to join one of the six colleges: Revelle, Muir, Marshall, Warren, Roosevelt, and Sixth. Suppose there are 24 incoming students, including Winona, Xanthippe, and Zelda. It cannot be assumed that all colleges will be assigned four students; since each student’s assignment is random, some colleges may be assigned more students than others.
Please leave your answers as unsimplified expressions with factorials, exponents, permutations, combinations, etc.
a) All 24 incoming students get called up one at a time to be assigned to a college. How many possible orders of all 24 students have Winona as the first student called?
b) How many possible orders of all 24 students have Zelda, Xanthippe, and Winona (in any order) as the first three students called up to wear the sorting hat?
c) How many ways are there to assign all 24 students to colleges such that Zelda, Xanthippe, and Winona all get assigned to Muir? Here, and in what follows, the order in which the students are assigned does not matter.
d) How many ways are there to assign all 24 students to colleges such that Zelda, Xanthippe, and Winona all get assigned to the same college?
e) How many ways are there to assign all 24 students to colleges such that Zelda, Xanthippe, and Winona are assigned to different colleges?
f) How many ways are there to assign all 24 students to colleges such that exactly 4 students get assigned to Warren?
g) How many ways are there to assign all 24 students to colleges if each of the six colleges has room for only four incoming students?
h) How many ways are there to assign all 24 students to colleges if nobody is assigned to the same colleges as the person called up just before them?
i) What is the probability that Winona, Xanthippe, and Zelda are all assigned to Muir?
j) Suppose again that the students are called up one at a time. In how many possible orders of all 24
students does Zelda get called up some time before Xanthippe? Simplify your answer as much as possible, but let factorials remain unsimplified.

Match the study with the type of study design. A type of study design can be used more than once.

a. Cross-sectional study

b. Randomized controlled trial

c. Prospective cohort study

d. Ecological study

e. Retrospective cohort study

1.All UMD students are surveyed on the first day of class, asking about their current vaping use.

2. A group of adolescents are randomized to receive either a comprehensive sex education program or an abstinence-only program. Pregnancy rates are compared at at 3 years post-program.

3. A group of Baltimore City residents who were exposed to lead paint as children are followed over time and surveyed at regular time points about their incidence of cancer.

4. A telephone survey of P.G. County residents asking about their neighborhood access to healthy food.

Selection/Conditional Structure: Create a flowchart and pseudocode for the problem below:

Juan dela Cruz Restaurant is offering a 20% discount to all customers whose last name is also dela Cruz. Input the last name of the customer and the total amount due to the customer and then output the amount to be paid.

(C++ Program, choose only the LAST NAME)

Discuss the various options for sampling and cohort formation within epidemiologic cohort studies. As a practicing epidemiologist, how would you go about selecting the best sampling and cohort formation options for a particular study?

Suppose in a certain cohort study a researcher followed 360 college students who regularly smoked cigarettes, and 1200 college students who did not regularly smoke cigarettes. None of the subjects had peptic ulcers at the start of the study period. At the end of the study period, 90 of the smokers and 60 of the nonsmokers had at least one peptic ulcer. For simplicity, assume that none of the students died or left the study early. Also, assume the sample is representative of the population of college students in Nevada. Finally, suppose that 20% of college students in Nevada regularly smoke cigarettes.

1. In the smokers, what percentage of the risk for developing at least one peptic ulcer is directly attributable to smoking?

2. In the population of Nevada college students, what absolute amount of risk for developing at least one peptic ulcer is directly attributable to smoking?

3. In the population of Nevada college students, what percentage decrease in the risk for developing at least one peptic ulcer could be achieved by completely eliminating smoking?

Suppose in a certain cohort study a researcher followed 360 college students who regularly smoked cigarettes, and 1200 college students who did not regularly smoke cigarettes. None of the subjects had peptic ulcers at the start of the study period. At the end of the study period, 90 of the smokers and 60 of the nonsmokers had at least one peptic ulcer. For simplicity, assume that none of the students died or left the study early. Also, assume the sample is representative of the population of college students in Nevada. Finally, suppose that 20% of college students in Nevada regularly smoke cigarettes.

1. In the smokers, what percentage of the risk for developing at least one peptic ulcer is directly attributable to smoking?

2. In the population of Nevada college students, what absolute amount of risk for developing at least one peptic ulcer is directly attributable to smoking?

3. In the population of Nevada college students, what percentage decrease in the risk for developing at least one peptic ulcer could be achieved by completely eliminating smoking?

A researcher with the Department of Education followed a cohort of students who graduated from high school in a certain​ year, monitoring the progress the students made toward completing a​ bachelor's degree. One aspect of his research was to determine whether students who first attended community college took longer to attain a​ bachelor's degree than those who immediately attended and remained at a​ 4-year institution. The data in the table attached below summarize the results of his study. Complete parts​ a) through​ e) below.

a) What is the response variable in this​ study? What is the explanatory​ variable?

A. The response variable is the number of students. The explanatory variable is the time to graduate.

B. The response variable is the use of community college or not. The explanatory variable is the time to graduate.

C. The response variable is the time to graduate. The explanatory variable is the use of community college or not.

D. The response variable is the time to graduate. The explanatory variable is the number of students.

b) Explain why this study can be analyzed using inference of two sample means. Determine what qualifications are met to perform the hypothesis test about the difference between two means. Select all that apply.

A. The samples can be reasonably assumed to be random.

B. The sample sizes are not more than​ 5% of the population.

C. The samples are independent.

D. The sample sizes are large​ (both greater than or equal to​ 30).

E. The population is given to be normally distributed.

c) Does the evidence suggest that community college transfer students take longer to attain a​ bachelor's degree?

Use an α=0.01 level of significance. Perform a hypothesis test. Determine the null and alternative hypotheses.

A. Upper H 0H0​: mu Subscript community college Baseline equals mu Subscript no transferμcommunity college=μno transfer​,

Upper H 1H1​: mu Subscript community college Baseline greater than mu Subscript no transferμcommunity college>μno transfer

B. Upper H 0H0​: mu Subscript community college Baseline greater than mu Subscript no transferμcommunity college>μno transfer​,

Upper H 1H1​: mu Subscript community college Baseline less than mu Subscript no transferμcommunity college<μno transfer

C.Upper H 0H0​: mu Subscript community college Baseline less than mu Subscript no transferμcommunity college<μno transfer​,

   Upper H 1H1​: mu Subscript community college Baseline greater than mu Subscript no transferμcommunity college>μno transfer

D.Upper H 0H0​: mu Subscript community college Baseline equals mu Subscript no transferμcommunity college=μno transfer​,

   Upper H 1H1​: mu Subscript community college Baseline less than mu Subscript no transferμcommunity college<μno transfer

Determine the test statistic.

t=_______ ​(Round to two decimal places as​ needed.)

Determine the​ P-value.

​P-value=_______ ​(Round to three decimal places as​ needed.)

Should the hypothesis be​ rejected?

▼(Do not reject, Reject) the null hypothesis. The evidence ▼(does, does not) suggest that community college transfer students take longer to attain a​ bachelor's degree at the

α=0.01 level of significance.

d) Construct a 99​% confidence interval for mu Subscript community college Baseline minus mu Subscript no transferμcommunity college−μno transfer

to approximate the mean additional time it takes to complete a​ bachelor's degree if you begin in community college.

The confidence interval is the range from _______ to ________.​(Round to three decimal places as​ needed.)

e) Do the results of parts​ c) and​ d) imply that community college causes you to take extra time to earn a​ bachelor's degree?

No

Yes

A researcher with the Department of Education followed a cohort of students who graduated from high school in a certain​ year, monitoring the progress the students made toward completing a​ bachelor's degree. One aspect of his research was to determine whether students who first attended community college took longer to attain a​ bachelor's degree than those who immediately attended and remained at a​ 4-year institution. The data in the table attached below summarize the results of his study. Complete parts​ a) through​ e) below.

Determine the Test Statistic

T= ___ (round to two decimal places as needed)

Determine the P-Value

P-value= ___ (round to three decimal places as needed)

D) Construct a 95% confidence Interval for community college - no transfer to approximate the mean additional time it takes to complete a bachelor's degree if you begin in community college.

The confidence intervals in the range from ___ to ___

E) Do the results of parts c) and d) imply that community college causes you to take extra time to earn a bachelor's degree?

Yes or No

A researcher with the Department of Education followed a cohort of students who graduated from high school in a certain​ year, monitoring the progress the students made toward completing a​ bachelor's degree. One aspect of his research was to determine whether students who first attended community college took longer to attain a​ bachelor's degree than those who immediately attended and remained at a​ 4-year institution. The data in the table attached below summarize the results of his study. Complete parts​ a) through​ e) below.

Community College Transfer:

n:268

Sample mean time to​ graduate, in years 5.49

Sample standard deviation time to​ graduate, in years 1.144

No Transfer

n 1175

Sample mean time to​ graduate, in years 4.51

Sample standard deviation time to​ graduate, in years 1.013

a) What is the response variable in this​ study? What is the explanatory​ variable?

A.The response variable is the use of community college or not. The explanatory variable is the time to graduate.

B.The response variable is the time to graduate. The explanatory variable is the use of community college or not.

C.The response variable is the time to graduate. The explanatory variable is the number of students.

D.The response variable is the number of students. The explanatory variable is the time to graduate.

​b) Explain why this study can be analyzed using inference of two sample means. Determine what qualifications are met to perform the hypothesis test about the difference between two means. Select all that apply.

A.The sample sizes are large​ (both greater than or equal to​ 30).

B.The population is given to be normally distributed.

C. The samples are independent.

D.The sample sizes are not more than​ 5% of the population.

E.The samples can be reasonably assumed to be random.

​c) Does the evidence suggest that community college transfer students take longer to attain a​ bachelor's degree? Use an

alpha equals 0.01α=0.01 level of significance. Perform a hypothesis test. Determine the null and alternative hypotheses.

A.Upper H 0H0​: mu Subscript community college Baseline equals mu Subscript no transferμcommunity college=μno transfer​,

Upper H 1H1​:mu Subscript community college Baseline greater than mu Subscript no transferμcommunity college>μno transfer

B.Upper H 0H0​: mu Subscript community college Baseline greater than mu Subscript no transferμcommunity college>μno transfer​,

Upper H 1H1​: mu Subscript community college Baseline less than mu Subscript no transferμcommunity college<μno transfer

C.Upper H 0H0​: mu Subscript community college Baseline equals mu Subscript no transferμcommunity college=μno transfer​,

Upper H 1H1​: mu Subscript community college Baseline less than mu Subscript no transferμcommunity college<μno transfer

D. Upper H 0H0​:mu Subscript community college Baseline less than mu Subscript no transferμcommunity college<μno transfer​,

Upper H 1H1​:mu Subscript community college Baseline greater than mu Subscript no transferμcommunity college>μno transfer

What new technologies were important in the history of bridges?

Why did the Romans use elevated aqueducts instead of pipes to convey their water?

Which of the Grand Challenges for the 21st century do you believe is most important? why? which challenge do you believe to be the least important? why? what challenges do you believe should be added to the list why?