Business Statistics Group Assignment - The Task
The purpose of this assignment is to improve your understanding in choosing between and using methods to assess the relationship between variables and make comparisons across different segments. It will develop your skills in being able to critically think and enhance your analytical skills.
Specifically, we want you to access the Excel database provided on UTS Online that describes 400 mobile phone users and their experiences in shopping online using a range of different electronic devices. We then want you to investigate using the various tools you have been exposed to in Business Statistics and answer several managerial questions.
You must complete this as a group of three, four or five students. There are five questions that each group must complete.
Q1) Intention to use a smartphone to purchase: Apple vs Non-Apple Users
This question has several parts:
(a) Examine just the data relating to those who currently own or lease an Apple smartphone. Construct a confidence interval to describe the average intention to use their smartphone for purchasing products in the next month among current Apple users.
(b) Examine just the data relating to those who currently do not own or do not lease an Apple smartphone. Construct a confidence interval to describe the average intention to use their smartphone for purchasing products in the next month among such users.
(c) Do the confidence intervals overlap?
(d) What does your answer to (c) suggest about differences in the average intentions to use the smartphone for purchasing products in the next month between those who own or lease an Apple smartphone compared to those who do not?
Please note:
- As with all five questions, explain which variables you used as inputs into your answers
- In answering this question, you should clearly show the various inputs to the margin of error that you used to construct the two intervals rather than relying on any automatically generated margin of error (e.g., selecting Excel Descriptive Statistics dialogue box) which may instead be useful to check your answers.
- Clearly state any assumptions that you are making to undertake the question.
- As you have access to a computer, you will be expected to use a table-value that is accurate (not rounded). This selection of table should be based on your knowledge about the population parameters, which you should also state to justify your selection of table.
- Present any inputs and answers to two decimal places, but round your calculations only at the end though to avoid round error.
Q2) Apple and Samsung likeability
A manager has asked you to consider the likeability of Apple among consumers and how this is related to levels of likability observed for their competitor, Samsung.
a) First, examine the brand likeability scores for Apple and Samsung separately using a range of suitable summary statistics. Write a short interpretation of your findings about the distribution of likeability scores for each brand based on these statistics.
b) Without actually constructing them, describe how would the width and location of the two confidence intervals for the average likeability scores for each brand differ?
c) Examine the association between Apple likeability and Samsung likeability using a correlation coefficient. Write a short interpretation of this statistic for the manager.
d) Construct a scatter-plot of the two scores and write a short interpretation of what the graphic shows. You should discuss the graph in terms of those that really dislike Apple, those who are indifferent relative to others and those who really like Apple.
e) Do your answers in c) and d) agree? Write a short explanation for the manager for why this may be the case.
Q3) Apple Likeability and Age Segments
The local brand manager is interested in the common belief that Apple is well liked by younger consumers and not well liked by older consumers. The brand manager decides that a good benchmark is a likeability score of 50: brands scoring significantly more than 50, on average, are deemed to be "well-liked" and brands scoring significantly less than this benchmark, on average, are classified as "not very well-liked".
a) Test the hypothesis that Apple has a 'par' score - that is, it has an average likeability score that is not significantly different from a score of 50.
b) Test the hypothesis that Apple is "well-liked" among consumers that are less than 25 years of age.
c) Test the hypothesis that Apple is "not very well-liked" among consumers that are more than 65 years of age.
d) Write a short interpretation of the results that speculates on your findings in (a) based on the conclusions you reach in (b) and (c).
In testing your hypotheses, clearly state your hypotheses, whether you are conducting a one-tail or two-tail test, inputs into how exactly you determined your critical value and test-statistic, any assumptions made and clearly state your conclusions. Since you have access to a computer, you are expected to generate accurate critical values (reporting this to four decimal places).
Q4) Perceived Security in Payments via Mobile vs. PCs
Examine the proportion of consumers who agree with the statement "I am sure that my payment information will be protected if I were to use a smartphone to buy something". You can assume that anyone who scores five or more on the 7-point scale to be those who agree with the statement.
a) Report this proportion along with the sample size. Report this as a percentage to two decimal places.
b) Based on your response to (a) and knowledge of central limit theorem, show that you have sufficient evidence for the assumption that the sampling distribution of the sample proportion follows a normal distribution.
c) Construct a 95% confidence interval that describes the proportion of consumers who agree with the statement "I am sure that my payment information will be protected if I were to use a smartphone to buy something". You can assume that anyone who scores five or more on the 7-point scale to be those who agree with the statement. Also, please assume that you can use your findings in (b) to justify the use of the z-score of 1.96 to undertake this question. In other questions (i.e. Q1, Q2, Q3 or Q5) you should not make this assumption. Please note: In answering the questions above, you should clearly show the various inputs to the margin of error that you used to construct the confidence interval. State your final answer in percentage terms to two decimal places.
d) Undertake the same exercise a) through c) but focus on the proportion of consumers agreeing with the statement: "I am sure that my payment information will be protected if I were to use a personal computer to buy something".
e) Compare your answers in c) and d) and write a short interpretation of the findings for someone interested in consumers perceived security concerns regarding online payments using a mobile phone as opposed to a personal computer (PC).
Q5) Telstra and Employment Status
A manager is interested whether there is a significant relationship between whether someone uses Telstra as their chosen carrier and their current employment status. This question has several parts:
a) Present a joint frequency table that examines the joint outcomes relating to carrier and employment status
b) Present the following figures in a single table (HINT: use the same layout as the one used in part (a) with slight adjustment to the headings in the table):
I) The probability that someone takes a certain employment status given they use Telstra as their preferred carrier. Present these in percentage terms to one decimal place.
II) The probability that someone takes a certain employment status given they do not use Telstra as their preferred carrier. Present these in percentage terms to one decimal place.
III) The probability that someone has a certain employment status. Present these in percentage terms to one decimal place.
c) How do the three sets of figures presented in question (b) compare? What do they suggest about the nature of the relationship between choosing Telstra as a carrier and employment status?
d) Formally test whether such a relationship exists using contingency analysis. You should include:
I) A table of expected frequencies under the assumption of independence between the two events of interest (entries to one decimal place).
II) An additional table showing the inputs into the chi-square test statistic calculation such that the sum of the entries in the table represents the test-statistic (entries to one decimal place).
III) List any background information (e.g., how you obtained your degrees of freedom) to undertake the test and subsequent critical value.
IV) A comparison of the final test-statistic and critical value and subsequent statistical conclusion.
e) Write a short managerial conclusion about Telstra as a choice of carrier and whether this decision appears to be independent of the employment status of the consumer.
Assignment Files -
https://www.dropbox.com/s/szbkh90yj0f8kk6/Assignment%20Files.zip?dl=0