2-2016/2017 -m248

INSTRUCTIONS: The TMA consists of eight questions and it worth 20% of the total grade assigned to the course. It will be graded out of 100 marks divided amongst the eight questions. In your answers, please be sure to show all your calculations and to submit copies of your output when asked to use MS Excel or any other software/source.

Question 1: (14 points)

The course chair carried out a study of students’ performance and behavior over three years. The data collected is summarized below.
Semester Registered Students Withdrawals
(Drop) Final Exam Absentees Final Exam
Attendees Students failing the final exam
Fall 2013-2014 220 20 8 192 11
Spring 2013-2014 200 19 7 174 30
Fall 2014-2015 230 16 5 209 23
Spring 2014-2015 270 28 13 229 54
Fall 2015-2016 200 10 4 186 16
Spring 2015-2016 225 18 7 200 45

a) What does the sum of withdrawals, absences and attendances on the final exam represent?
b) Calculate in each semester the percentage of final exam failures out of those registered and comment on any pattern or trend that your results reveal.
c) Use MS Excel to draw a suitable chart to represent the number of registered students across the 6 semesters (time). Justify your choice for the type of graph.
A proper chart must contain (title, labels for axes, frequencies, etc….…)

Question 2: (20 points)

A special aptitude test is given to job applicants. The data shown here represent the scores of 10 applicants.

200 208 210 212 215 216 220 225 230 244
a) Calculate the sample mean of scores and the median of scores. 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 answer to 2 decimal places)
d) Consider below the boxplot of the given data, comment on its skewness.



e) If the company hires only the top 25% of applicants. Do you think Mr. X whose score is 229 has a chance to be hired? Justify your answer.

Question 3: (12 points)

The probabilities that a bakery has a demand for 2, 3, 4, or 5 birthday cakes on any given day
are 0.35, 0.40, 0.15, and 0.1, respectively.

# of Cakes: X 2 3 4 5
Probability: P(X=x) 0.35 0.4 0.15 0.1

a) What is the expected value of the number of sold cakes?
b) What is the standard deviation of the number of sold cakes? (Round your answer to 2 decimal places)
c) Determine the Cumulative Distribution Function?
d) What is the probability of having more than 4 cakes sold in a day?

Question 4: (14 points)

A manufacturer of television sets has found that for the sets he produces, the lengths of time until the first repair can be described using a normal distribution with a mean of 4.5 years and a standard deviation of 1.5 years.

a) For a Quality Control inspection, a TV was randomly selected for assessment, what is the probability that the length of time until the first repair is between 4 and 6 years?
b) For a sample of 10 randomly selected TVs, what is the probability that the mean length of time until the first repair is less than 3.5 years?

Question 5: (14 points)

A group of automotive engineers decided to conduct a study of school buses and found that for a sample of 35 buses, the average stopping distance of buses traveling at a specific speed was 1.80 m and a standard deviation of 0.2 m.

a) Construct a 95% confidence interval for the mean of stopping distance for school buses travelling at the specific speed. (Round your answers to 2 decimal places)
b) Interpret the results of part a.

Question 6: (14 points)

A physician states that jogging and sports in general increases the maximum volume of oxygen uptake. A sample of 15 joggers has a mean of 40.6 milliliters per kilogram (ml/kg) and a standard deviation of 6 ml/kg.

a) Construct a 95% confidence interval for the average maximum volume of oxygen uptake for joggers. (Round your answers to 2 decimal places)
b) Interpret the results of part a.

Question 7: (12 points)

An English teacher wishes to see whether a new grammar program will reduce the number of grammatical errors her students make when writing a two-page essay. The data are shown below.
Student Errors Before program Errors After program
1 12 9
2 9 6
3 0 1
4 5 3
5 4 2
6 3 3
7 5 5
8 10 6
9 1 0
10 2 2

Use an open source (online) to construct the 95% confidence interval for the mean of the difference between the two populations (Errors Before program and Errors After program)
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