m248 The ministry of higher education in a certain country is conducting a study on universities’ performance and recruiting. The following data was collected.

Question 1: (15 points)

The ministry of higher education in a certain country is conducting a study on universities’ performance and recruiting. The following data was collected.

University Rank Graduates of 2017 # of Faculty members # of Enrolled  Students
University S B+ 1450 100 7850
University T A+ 920 150 5500
University M B+ 1350 110 7400
University N B+ 1320 90 8350
University V B 910 85 6610
University X A 1105 105 5560
University Y C 850 80 7856
University Z A 980 124 4563

a) For each university, calculate the ratio of faculty members to enrolled students in percentage form (Round your percentage to two decimal places).
b) For each university, calculate the percentage of graduates of 2017 relative to the number of enrollments in each university (Round your percentage to two decimal places).
c) Use MS Excel to draw a suitable chart to represent the data in the table below. Justify your choice for the type of graph.  
A proper chart must contain (title, labels for axes, frequencies, data values, etc….…)

University Rank Number of Universities
A+ 5
A 7
B+ 12
B 4
C+ 2

Question 2: (20 points)

Shoplifting is a serious issue at a supermarket found in a specific neighborhood. Consider below the number of shoplifts recorded daily after security cams installations over a period of 10-days.
     4         4           5  5    5       6            6 8             8              9  


a) Calculate the sample mean of the number of shoplifts and the median of the number of shoplifts. What can you say about the skewness of the data set? Justify your answer.
b) Would any of the given numbers be considered an outlier?  Justify your answer.
c) Determine the sample variance. (Round your final answer to two decimal places)
d) Consider in the next page the boxplot of the given data, comment on its skewness.  


Question 3: (13 points)

The probabilities that a randomly selected home has garage space for 0, 1, 2 or 3 cars are shown in the table below.

garage space for  X cars: X 0 1 2 3
Probability: P(X=x) 0.4 0.3 0.2 0.1

a) What is the expected value of the number of cars having garage space?
b) What is the standard deviation of the number of cars having garage space?
c) Determine the Cumulative Distribution Function?
d) What is the probability that a randomly selected home has a garage space for at least one car?

Question 4: (14 points)

A recent study of the lifetimes of cell phones found the average to be 24.3 months. Assume the variable is normally distributed with a standard deviation of 2.6 months.
a) What is the probability that the lifetime of a randomly selected phone will be between 23 and 26 months?
b) If a company provides its 33 employees with a cell phone, find the probability that the sample mean of lifetime of these cell phones will be less than 23.5 months?

Question 5: (14 points)

A small urgent care center found that in a sample of 20 days they can see an average of 18 patients daily with a standard deviation of 3.2.

a) Construct a 90% confidence interval for the mean of the number of patients that the center can care for in one day. (Round your final answers to 2 decimal places)
b) Interpret the results of part a.

Question 6: (14 points)

In a random sample of 200 people, 154 said that they watched educational television. The television company wanted to publicize the proportion of viewers.

a) Construct a 95% confidence interval for the proportion of people who watched educational television. (Round your final answers to 2 decimal places)
b) Interpret the results of part a.


Question 7: (10 points)

A random sample of ten local banks shows their deposits (in billions of dollars) 3 years ago and their deposits (in billions of dollars) today. A financial analyst would like to study the change in deposits over the past three years.

Bank 3 Years Ago Today
1 11.42 16.69
2 8.41 9.44
3 3.98 6.53
4 7.37 5.58
5 2.28 2.92
6 1.10 1.88
7 1.00 1.78
8 0.9 1.5
9 1.35 1.22
10 1.25 2.81

Use an open source (online) to construct the 95% confidence interval for the mean of the difference between the two populations (deposits 3 years ago and deposits today). (Paired Data)

Use print screen and paste your output to your TMA.

Examples of open sources:
http://www.physics.csbsju.edu/cgi-bin/stats/Paired_t-test_form.sh?nrow=10
https://www.graphpad.com/quickcalcs/ttest1.cfm