STATS USING MINTAB 17 or 18

Assignment 1 (Chapters 1 - 4, 6)

STAT 2606 - Business Statistics I (2020 Fall) School of Mathematics and Statistics, Carleton University

Due Date and Time: Monday, November 2, 2020, 11:59 pm Total Marks: 100

Instructions for Submission

• You MUST show your detailed work and include necessary MINITAB outputs to earn full marks

• The assignment MUST be submitted to the cuLearn by the due date and time

• The only acceptable format of the assignment is ”pdf”. Any type of file other than ”pdf” will NOT be evaluated

• Only one pdf file needs to be submitted. Multiple files will not be evaluated. In case of multiple submissions, only the latest submission will be considered as final submission

• Answers could be ”typed” or ”handwritten”. In case of handwritten assign- ment, please ensure that the handwriting or scanned document is legible

• NO EMAIL SUBMISSION WILL BE ACCEPTED UNDER ANY CIRCUM- STANCE. Any assignment that needs to be evaluated MUST be submitted to the course site at the cuLearn

• Lack of access to MINITAB will NOT be an acceptable reason for late sub- mission

• It is assumed that students will be using the following options to use MINITAB (any version of MINITAB can be used to work on assignment):

– Using MINITAB at remote servers (a maximum of 40 users can access concurrently)

– Purchased MINITAB with a e-book package

– Rented MINITAB licence for one year

– It is strongly recommended that students work on assignment well be- fore the deadline to avoid issue pertaining to access to Virtual Desktop Interface (VDI)

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Q1: [4]Self-isolation for Coronavirus

In the context of the current pandemic situation, the Ottawa Health Agency (OHA) was interested to know how Ottawa residents support their recommended self-isolation instruc- tions related to the novel Coronavirus. They commissioned a professional agency to do a survey of 1000 individuals living in the city in March 2020 and obtained the following results:

Support of OHA Self-Isolation Instructions

Support Oppose Total Returning Travellers 69 81 150

Non-travellers who had contact 243 207 450 Non-travellers who did not have contact 300 100 400

(a) [1]What is the population of interest?

(i) Ottawa residents who participated in the survey

(ii) Ottawa residents in March 2020

(iii) Ottawa citizens

(b) [1]What is the appropriate statistic for assessing the support for OHA recommended self-isolation instructions related to novel Coronavirus?

(i) Mean

(ii) Median

(iii) Proportion/Percentage

(c) [1]If OHA approximates the probability of supporting/opposing the self-isolation in- structions of different sub-populations (travellers and non-travellers) in March 2020 based on this survey, which method of assessment is used?

(i) Classical Probability

(ii) Empirical Probability (Relative Frequency Approach)

(iii) Subjective Probability

(d) [1]Which of the following best describes the purpose of this exercise?

(i) Descriptive statistics about a sample

(ii) Inferring information about a population from information about a sample

(iii) Descriptive statistics about a population

(iv) Inferring information about a sample from information about a population.

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Q2: [25]Top Visited Sites in December 2003

The most visited site on the internet is Yahoo!, which boasted 111,271 thousand unique visitors in December 2003. The number of unique visitors at the top 25 sites are shown in the table:

Site Unique Visitors (Millions) Yahoo! Sites 111.3

Time Warner Network 110.5 MSN-Microsoft Sites 110.0

eBay 69.2 Google Sites 61.5 Terra Lycos 52.1

Amazon Sites 45.7 About/Primedia 42.6 Excite Network 25,1 CNET Networks 25.1

Walt Disney Internet 25.1 Viacom Online 24.7

American Greetings 24.4 Weather Channel 23.8 Real.com Network 22.3

Verizon Communications 22.1 Wal-mart 21.4

Shopping.com Sites 21.3 Symantec 19.9

AT&T Properties 17.5 InfoSpace Network 17.3 Monster Property 17.3

EA Online 16.8 SBC Communications 16.5

Sony Online 16.5

(a) [2]Can you tell by looking at the data whether it is roughly symmetric? or is it skewed?

(b) [15]Calculate the mean, median, standard deviation, 25th and 75th percentile. Use the measures (mean, median) to decide whether or not the data are symmetric or skewed. Which centre of location (mean, median) do you recommend? Justify.

(c) [4]Draw a box plot to describe the data and identify the outliers, if any. Explain why the box plot confirms your conclusions in part (b)

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(d) [2]Create the data set in MINITAB and find the descriptive statistics (mean, median, standard deviation, 25th percentile and 75th percentile) and boxplot using MINITAB and include your output here.

(e) [2]Suggest an appropriate graph to describe graphically the variable Visitors, draw the graph using MINITAB and include the output here.

Q3: [16]TV Commercials

The mean duration of television commercials on a given network is 75 seconds, with a stan- dard deviation of 20 seconds. Assume that durations are approximately normally distributed.

(a) [5]What is the approximate probability that a commercial will last less than 35 seconds?

(b) [5]What is the approximate probability that a commercial will last longer than 55 sec- onds?

(c) [6]Can you use Chebyshev’s Theorem to describe the data? Why or why not? If yes, use Chebyshev’s Theorem to make a statement about the percentage of commercials that lasts between 45 and 105 seconds.

Q4: [25] Music Streaming

When customers subscribe to a music streaming service, they have 2 options (a) a free service (b) a premium service costing $12/month. Based on customer data from the most recent year, the company finds that 70% of new customers choose the free service. At the end of their first month, subscribers have 3 options (i) continue their existing service, (ii) switch to the other service (iii) discontinue the service. The past years customer data also shows that the proportions of customers with the free service in their first month who choose these 3 options are (i) 60% (ii) 30% (iii) 10%. Also, the proportions of customers with the premium service in their first month who choose these 3 options are (i) 80% (ii) 10% (iii) 10%.

(a) [1]What method of assessment was used to estimate the proportion (or probability) in the question?

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(b) [4]What is the probability of a customer dropping the service in their second month?

(c) [4]Is dropping the service in the second month independent of having the free service in the first month?

(d) [4]What is the probability that a customer had originally subscribed to the free service in their first month given that he/she has the premium service in their second month?

(e) [4]What is the probability that a customer has premium service in the first month or premium service in the second month?

(f) [4]Assuming that free or discontinued service brings $0 revenue, what is the expecta- tion and variance of revenue from one customer in their first month?

(g) [4]What is the Coefficient of Variation of the revenue from one customer in their first month?

Q5: [15] Stock Market

Investing in the stock market requires a great deal of analysis. Generally, amateur investors simply guess when they invest in. Assuming that stocks come in two varieties, ‘Good’ and ‘Bad’ and every time one invests in a new stock, the investment has the same probability of 0.3 that it will a ‘Good’ one.

(a) [2]If an amateur investor invests in 10 stocks, what will be the long term average and standard deviation of the number of ‘Good’ stocks?

(b) [5]If the amateur investor wants to calculate the probability that he will have invested in at least 3 ‘Good’ stocks, what value should (s)he obtain?

(c) [5]What is the probability that the investor will invest in less than 2 ‘Bad’ stocks?

(d) [3]Calculate the probabilities of part (b) and (c) using MINITAB and include the MINITAB output here. Do you have the same results?

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Q6: [15]Service Depot

A large service depot has a clientele of large companies with extensive computer equipment. The average number of service calls they receive every day over an 8-hour period is 3. They employ three highly trained technicians and other supporting staff. Every service call re- quires one technician for the entirety of the day on which they are called.

(a) [2]What is the probability that on a given day, there will be exactly 4 service calls?

(b) [5]What is the probability that there will be more than three calls in one day so that the three technicians will not be sufficient?

(c) [5]One day, there were no service calls in the morning and one technician was allowed to take the afternoon off. In the remaining four hours of the afternoon, what is the probability that there will be more than two service calls in the afternoon so that the service depot will not be able to meet the full service needs with only two technicians?

(d) [3]Please find the probabilities of part (a), (b), and (c) using MINITAB and include your output here.

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