The two-page report should start with an intro paragraph of the general description and motivation of the project and end with a summary paragraph of the conclusions you would like to show

Please submit the Excel worksheet and the written report.
A high school has a population of 200 students. The school is considering opening a new
on-campus cafe. The opinions of the 200 students [in Column B] are stored in the Excel file
StudentOpinion.xlsx. If a student is in favor of a new on-campus cafe, his/her/their opinion is
coded as 1. Otherwise, his/her/their opinion is coded as 0. We denote the coded opinion [in
Column C] of a student as xi, i = 1, …, 200. The true proportion of students who are in
favor of a new on-campus café equals ?????? ?? 1′?
200
=
∑ ??
200
?=1
200
. Suppose an analyst
who doesn’t have access to this spreadsheet, would like to conduct a study about the students’
opinions. She randomly selected five students [with replacement, i.e., one student can be
repeatedly selected.] and asked their opinions about having a new on-campus cafe. Define a
random variable x: the number of students who support the proposal of a new on-campus
cafe in the sample of five students.
Complete the following tasks.
1. Compute the true proportion of students who are in favor of a new on-campus cafe.
We will see in Chapters 6 and 7 that this proportion is called the population/binomial
proportion. [Excel: = sum(data)/200, where data is the range of the data set, C2:C201
in this question.]
2. Now, we will simulate the value of x 300 times. This means we repeat the experiment
(randomly select five students) 300 times and record the value of x each time. [Excel:
To perform the experiment once (i.e., take one sample of five students),
SUM(INDEX(data,RANDBETWEEN(1,200))+INDEX(data,RANDBETWEEN(1,200))
+INDEX(data,RANDBETWEEN(1,200))+INDEX(data,RANDBETWEEN(1,200))
+INDEX(data,RANDBETWEEN(1,200)))
Explanation of the Excel functions:
(a) RANDBETWEEN(1,200)): randomly select one student from 200 students.
(b) INDEX(data,RANDBETWEEN(1,200)): locate the opinion of the randomly selected student.
(c) SUM(INDEX(data,RANDBETWEEN(1,200))+INDEX(data,RANDBETWEEN(1,200))
+INDEX(data,RANDBETWEEN(1,200))+INDEX(data,RANDBETWEEN(1,200))
+INDEX(data,RANDBETWEEN(1,200))): sum up the coded opinions of the five
randomly selected students].

3. Now, we have 300 observations of x. Compute the relative frequencies that x = 0,
x = 1, x = 2, x = 3, x = 4, and x = 5. These relative frequencies are estimated
probabilities for each possible value of x. If we repeat the sampling procedure in
Question 2 for a very large number of times (say, thousands or millions of times), the
estimated probabilities will be very close to the true probabilities, P(x = 0), P(x = 1),
…, P(x = 5).
4. Use “bar chart” function in Excel to plot the relative frequency histogram of the data
(300 observations) you generated for x.
5. Compute the sample mean and sample standard deviation of the 300 data values you
generated for x. [Excel: average(data), stdev(data)]
6. The probability that a randomly selected student is in favor of a new cafe is 0.57
(the proportion you calculated in Question 1). The selections of the five students are
identical and independent five trials. Thus, from what you have learned in class, this
experiment is a binomial experiment and x follows a binomial distribution with n = 5
trials and p = 0.57. Now, let’s use Excel to compute the exact probabilities of x, i.e.,
?(?) = (
5
?
) (0.57)
?
(1 − ?)
?−?
, ? = 0, 1, 2, 3, 4, 5. (If done by hand.)
[Excel: binom.dist(k,5,0.57,FALSE), when “FALSE”, Excel computes p(k); when “TRUE”,
Excel computes Pr(x ≤ k).]
7. Use “bar chart” function in Excel to plot the exact probability distribution of x. Compare
it to the relative frequency histogram in Question 4. Are they close? Explain.
8. Use Excel to compute the exact probability that fewer than two students in the sample
are in favor of a new cafe. [Excel: binom.dist(1,5,0.57,TRUE). Can you tell why the
first argument is 1 not 2?]
9. If the analyst randomly selected ten students instead of five, would you be surprised to
observe that fewer than three students support having a new cafe? Explain