calculate the mean and standard deviation of each investment, assume that both returns come from independent samples, are both normally distributed and that the true (but unknown) variances are not the same.

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Statistics
Paper, Order, or Assignment Requirements

Question 1

Below are the quarterly returns on investment (in £000s) of two different investment projects which had the same initial outlay. There is a sample of 16 quarters of returns and your manager has asked you to investigate the relative performance of each project. In particular, your manager suspects that ‘Investment B’ outperforms ‘Investment A’ and she would like you to test this hypothesis. Perform an appropriate statistical test that incorporates your manager’s hypothesis.

Hint: in this question you will need to calculate the mean and standard deviation of each investment, assume that both returns come from independent samples, are both normally distributed and that the true (but unknown) variances are not the same.

[25 marks]

Quarter Investment A Investment B
2012Q1 93 85
2012Q2 90 115
2012Q3 82 91
2012Q4 84 118
2013Q1 92 97
2013Q2 95 109
2013Q3 87 103
2013Q4 91 106
2014Q1 91 100
2014Q2 97 100
2014Q3 83 68
2014Q4 96 97
2015Q1 99 92
2015Q2 91 106
2015Q3 90 97
2015Q4 86 87

Question 2

The table below represents the results from 100 different marketing campaigns performed over three different products; the table splits between the products (Product A, B and C), and between the success of the marketing campaign, segregating between those which demonstrate: no increase in sales before and after the campaign; and, an increase in sales compared to before the campaign.

Your manager thinks that the success of the marketing campaigns is different across different products, but she does not know if this result is statistically significant. Test this hypothesis with an appropriate statistical test.

[20 marks]

Product A Product B Product C
No increase in sales 12 7 40
Increase in sales 13 13 15
Question 3

The head office of a large retailer feels that one of its stores is outperforming the overall sales of their UK shops in general. They would like to promote this fact, and further, try to learn and understand more about their success. However, they want to know that this result is a fair interpretation of the data, and ask you to perform a test of statistical significance on this result.

The national monthly sales for the retailer are normally distributed with a mean of £69,000 and a standard deviation of £11,500. For the individual store in question, there are data for 12 months of sales which has a sample mean of £80,000. Perform a statistical test on the claim that the store is outperforming the UK average, assuming that monthly sales are normally distributed.

[15 marks]

Question 4

For one of the questions above, prepare a short report on the results. Do this assuming a wide audience with differing levels of knowledge in the area of statistics and hypothesis testing (therefore, explain the processes involved in simple but formal language). In particular, discuss the following:

The idea behind hypothesis testing and why this is important;
The process performed in order to get the results, the key assumptions in this process, and the appropriateness of these assumptions to the question;
The result, how to interpret the result, and the meaning of the p-value.

Within this, feel free to bring in other knowledge you have from the question which you did not apply in previous questions that you feel would best describe the process and result to a wide audience (for example, calculating other factors from the numbers and/or graphs). This is meant to be a (very brief) report which you would happily present in a business format.

Although there is no formal word limit, 500 words is a good length in order to bring together all arguments required for this question.

[40 marks]

 

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Write an analysis, which draws conclusions from the data, linking back to the theoretical context and aims of the investigation.

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Using Statistics to Carry Out an Investigation
Paper, Order, or Assignment Requirements

Assignment Brief (Word count 1000 1500 words)

You are strongly advised to select a theme which is related to the academic content of your chosen Diploma. You must ensure that the chosen theme offers sufficient scope for investigation, and allows you to meet both the Learning Outcomes and the Grade Descriptors.

The assignment should consist of a written introduction, which describes the method by which sufficient and accurate data is to be collected. This data should be processed, using a range of graphical and statistical techniques appropriate for the purpose of the investigation, and to the level of study. (LO 1)

Data should be presented in a variety of formats appropriate for the purpose of the investigation, and to the level of study. The results should be interpreted. (LO 2)

Write an analysis, which draws conclusions from the data, linking back to the theoretical context and aims of the investigation. (LO 2)

Write a conclusion, which describes the limitations of the investigation, and suggest improvements which could be made. (LO 3)

 

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Identify (and clearly indicate them in your submission) a minimum of three lenders Kyle could borrow the money from and discuss the mortgage alternatives available and the respective terms and applicable interest rates

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Financial mathematics and statistics modelling
Paper, Order, or Assignment Requirements

Question 1: (25%)

Kyle Dier is looking to buy his first home and through savings and a gift from his parents he has managed to raise £80,000. Kyle has identified two possible properties, a one bedroom flat in the centre of town that costs £250,000 and a three-bedroom house outside of town that costs £400,000 and he’s decided to ask for your help identifying the best mortgage offers he can choose.

Required:

Identify (and clearly indicate them in your submission) a minimum of three lenders Kyle could borrow the money from and discuss the mortgage alternatives available and the respective terms and applicable interest rates;
For the most favourable rate for each type of mortgage, calculate the monthly payment Kyle would need to make for each of the properties he’s looking to possibly buy if he chooses to take out a 20-year mortgage;
Kyle believes it is highly likely that we will receive £50,000 in two years’ time and if he does, he will use the money to make a partial payment of the mortgage. For both options in b) and considering the payments he will have done by then as well as the one-off partial payment, calculate the monthly payments for the remaining 18 years of the mortgage.
Make a recommendation on the property Kyle should buy purely on financial terms and identify what other factors should be taken in consideration when making the final decision.

Question 2: (10%)

Due to the continued low level of sales Toys For You, a wholesaler of toys and games has experienced in the last three years, the management has been conducting a review of its stock ordering system. The management of the company has asked each of the analysts in its finance department, to look at one of its product lines, and you were asked to look at board games. Having made your research, you have determined that it is uncertain when the recovery will start, so you have established the following demand scenarios for the next 12 months:

Scenario Crisis Continues Slow Recovery Medium Recovery Fast Recovery
Probability 10% 30% 40% 20%
Demand 50,000 65,000 85,000 100,000

Considering the cost per order is £50 and the average carrying cost per unit is £1.50:

Determine the Economic Order Quantity given the data above.
Produce sensitivity analysis assuming a change of up to 10% up or down on each of the factors individually and on all factors simultaneously.
Make a final recommendation to the board of the company, as to the number of units it should include in each order.
Question 3: (20%)

A company that manufactures electrical appliances is looking at one of its lines (washing machines), where it offers three different levels of specification: Basic which sells for £250, Medium which sells for £450 and Luxury which sells for £700. The production of each machine goes through four different stages and you have been provided with the following data table:

ProcessMachine Basic Medium Luxury Cost per hour Max. Available
Forming 1.5 hours 3 hours 7 hours £5.50 6,500 hours
Machining 5 hours 8 hours 14 hours £7.50 18,000 hours
Assembly 2.5 hours 4.5 hours 8 hours £9.50 8,500 hours
Testing 2 hours 2 hours 2 ½ hours £12.00 5,200 hours

The marketing department has also done some market research and believes demand for each of the models is limited to 1,450 units of the basic model, 900 of the medium and 750 of the luxury. You are required to:

Formulate this problem as a linear program and use Excel’s Solver to arrive at a solution, identifying what is the maximum profit the company can achieve in the washing machine product line.
How would your answer change if the following happened:
Maximum demand for Medium model was 1,000; OR
Maximum available Assembly hours were 9,500.
Write a report with a recommended production and marketing plan for the company.

Question 4: (15%)

Given the data included in the excel file “Assignment FM&BS 1516 Data”:

Summarise the distribution of family income and house price and comment on the results?
Is there evidence that the average house price is £500,000? Justify
Based on this sample, provide a 90% and a 99% confidence interval for the Family income and explain and justify the difference between the two intervals.
Would you expect to find a relationship between the two variables under study? If so, what type of relationship would you expect?
Does this data provide evidence to support your answer to part d)?

Question 5: (20%)

The management of Make More plc, a manufacturer of low cost electronic products, has seen a significant increase in the company’s activity over the last two years.

The company now has to decide whether to undertake a potential investment to make three additional products using a new technology. In order to undertake this investment, Make More is looking to lease a new facility for the next six years, after which it is expected that the technology will be obsolete. The forecasted cash flows put together by the management of the business are as follows:

Sales of the three products in year one will be 50,000 units at an average price of £55;
Sales volume is expected to grow at 20% a year for the first three years, and decrease at 25% a year for the remainder of the project;
Cost of sales will be 65% of sales;
Selling and administrative expenses specific to this project will be £450,000;
The lease rent will be £150,000;
In order to manufacture the three products, Make More is going to buy equipment worth £1m. This equipment is expected to have a scrap value of £150,000 in six years time;
Equipment will be depreciated using straight line depreciation (Note: depreciation is not a cash flow, but since it is a cost, it affects the tax calculation and tax paid is a cash flow);
Corporate tax rate is 20%;
The current cost of capital of Make More is 15%, but this project is considered to be riskier and the cost of capital for companies with comparable levels of risk is 20% higher.

Required:

Discuss and compare the different types of investment appraisal methods Make More can use, including a discussion of the advantages and disadvantages of each.
If Make More had a rule that all investment projects need to payback within 2 years, would this project be accepted or rejected? Comment.
Using NPV and IRR, make a recommendation on whether Make More should go ahead with the investment.

 

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Is the Internet Creating a “dumber” and “less sociable” society?

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STATISTICS
Paper, Order, or Assignment Requirements

Write a 2-3 page paper discussing the measurement scale for each question in the survey developed in the Unit III assignment.

1. Decide if you will use composite scale score or a summated scale score. Justify your decision.
2. How will you measure reliability, validity, and sensitivity?
3. Explain how you will deal with ethical dilemmas during the research process (confidentiality, anonymity, conflicts of interest, informed consent, debriefing, experiments on human subjects, and so forth).

Is the Internet Creating a “dumber” and “less sociable” society?

Questionnaire

Internet users and usage varies from survey to survey and individual to individual. The current survey is based on internet habits and user preferences. This survey will take approximately 15 minutes to complete. All data will be used for research purposes only and will be destroyed after data is reviewed and analyzed.

What age group do you belong to?
Under 15
18-21
22-25
26-30
31-35
36-40
41-50
over 50

What is your gender?
Female
Male

What is your “primary” status?
student
full-time employment
part-time employment
self-employed
unemployed

on average, how many hours per day do you spend on the
internet?

less than 1 hour
1-2 hours
2-3 hours
3-4 hours
4-5 hours
more than 5 hours

Which of the following devices do you most use to connect to the internet?
computer tablet
smartphone
laptop computer
desktop computer
other (please specify) ____________

Where are you most often when you use the internet?
outside
home
school
library
work
bookstore
café/coffee shop
friend/family’s house
other (please specify) ___________

If at home, what room do you use the internet the most?
office
living room
dining room
bedroom
other (please specify) ____________

What are the top three things you do the most online?

____________________________

____________________________

____________________________

How oven do you use the internet for?

What source do you get your research information from?
library
on-line library
web-browsing
other (please specify) ____________

Approximately how many on-line contact you have? ____________

How many on-line contacts do you have that you have not met in the real world? ___________

How do you communicate with your off-line friends/family?
voice call (mobile)
voice call (land line)
video call (skype, Facetime, etc.)
e-mail
text messaging

How often do you contact your offline friends?
daily
weekly
monthly
less than once a month

When out with friends/family doing other activities, do you?

 

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Create a scatter plot to show this relationship between education and beginning salary Determine the correlation between the variables

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Statistics
Paper, Order, or Assignment Requirements

Unit 4 PROJECT

The Unit 4 project is located in Doc Sharing. You should download this Word document as well as the MM305 Project Data Sets and save them to your computer (I recommend you create a file for your MM305 projects), using your name in the file name. For example, if Jimmy Buffett were to download the MM305 Unit 4 project he would use “Save As” and save the project as “Jimmy Buffett Unit 4 Project”. He would save this file in his MM305 folder. After completing the Unit 4 project you should submit it using the Unit 4 Project Dropbox.

Submitting your Project:

When you are ready to submit your project, click on the Unit 4 Dropbox and complete the steps below:

•Click the link that says Submit an Assignment .
•In the “Submit to Basket” menu, select Unit 4 Project
•In the “Comments” field, include at least the file name of your project.
•Click the Add Attachments button.
•Follow the steps listed to attach your Word document.
•To view your graded work, come back to the Dropbox or go to the Gradebook after your instructor has evaluated it. Click the Dropbox to access it.

. For each the following variables from the Salary Data Set provide the measures of location and measures of dispersion for the following variables:

Previous Experience
Education
Which variable has the greatest relative variability?

You are the manager of a high-end ladies fashion store. For the past few months you have been gathering data and found that 45% of persons entering the store actually make a purchase. Assume these data follow a Binomial Distribution and use Excel to calculate the following binomial probabilities:
If 15 people enter the store, what is the probability that 9 of them will make a purchase?
What is the probability that at least 6 of the 15 people will make a purchase?

Using the Salary Data Set what is the probability of randomly selecting one individual (male or female) with a current annual salary of over $55,000?

The time required to complete a project is normally distributed with a mean of 80 weeks and a standard deviation of 5 weeks. The construction company must pay a penalty if the project is not finished by the due date of the contract. If a construction company bidding on this contract wishes to be 90 percent sure of finishing by the due date, use the NORMINV Excel Function to determine what due date (project week #) should be negotiated?

In a state lottery participants select 6 numbers between 1 and 49. At the end of the week, the state lottery commission randomly draws 6 numbers between 1 and 49. How many different possible winning number combinations could be drawn by the lottery commission?
From the Salary Data Set and assuming that the salary data is a random sample from the population of salaries from the multi-national company use the 90% confidence level in PHStat to estimate the mean current salary for company executives.
The 90% confidence level is:
If you were to change the confidence level to 95%, what would happen to the confidence interval?

Using the Salary Data Set,

Create a scatter plot to show this relationship between education and beginning salary
Determine the correlation between the variables

Explain why rejecting the null hypothesis does not make the alternative hypothesis true.

What is the purpose of statistical inference?
What is the difference between sampling error and the standard error of the mean?

You are a consultant working for Kaplan Consulting. The Director of Human Resources for a multi-national company has requested help in investigating a pay discrimination complaint brought by a female executive. The company provided the data in the Salary Data Set. Use PHStat and the appropriate t test, to investigate the claim of pay discrimination in the current salaries. Be sure to include:
Your null and alternative hypotheses;
The level of alpha you elect to use and why in terms of Type I or Type II error;
Show the output from the analysis;
Your interpretation of the results; and
A written statement to the director of Human Resources as to whether they should be concerned about the complaint.

 

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Assume that the final scores in a statistics unit follow a normal distribution with mean 72 and standard deviation 10. Use SPSS to find the proportion of the scores less than 50.

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Introduction to statistics
Paper, Order, or Assignment Requirements

Computer Assignment

[a] Your assignment should be done individually only.
[b] Your student ID must be put on the top right-hand corner of every page.
[c] Both the two questions must be attempted, using SPSS or another package.
[d] All graphs should be presented within the body of the assignment under the relevant questions, NOT at the end of the assignment in an appendix.
[e] Your assignment is expected to contain no more than 7 single-sided pages.
[f] A soft copy of your assignment is required to be submitted onto the Moodle site before 5pm Friday 15 April 2016; Email submission is NOT acceptable. After the submission of your assignment, there will be a number of validation questions available on Moodle based on or related to your assignment, which MUST be answered and marked before 11:59pm Sunday 17 April 2016.

Question 1.
Assume that the final scores in a statistics unit follow a normal distribution with mean 72 and standard deviation 10. Use SPSS to find (and present the code as part of your solution):
[a] the proportion of the scores less than 50.
[b] the proportion of the scores larger than 65 but less than 85.
[c] the minimum score for being in top 10%.
[d] the probability for the average of 5 scores to be larger than 80.
=================================================

Question 2.
People with diabetes must manage their blood sugar levels carefully. They measure their fasting plasma glucose (FPG) several times a day with a glucose meter. Another measurement, made at regular medical checkups, is called HbA. This is roughly the percent of red blood cells that have a glucose molecule attached. It measures average exposure to glucose over a period of several months.
The Excel file called Diabetes has data on both measures of glucose level in diabetics for 18 diabetics five months after they had completed a diabetes education class.
[a] Construct a histogram to study the FPG variable, with brief comments.
[b] Find the correlation coefficient between the two variables FPG and HbA.
[c] Present a scatter plot of FPG vs HbA with the least-squares equation and brief comments.
[d] Identify one outlier in the y direction and one outlier in the x direction, and remove them from the dataset. Find the correlation between FPG and HbA, and draw a scatter plot of FPG vs HbA with the least-squares equation. How does the correlation and the scatter plot change after the two outliers have been removed? Why?
[e] Compare the two least-squares equations with their R square values, and identify which one is better. Why?
[f] Which subject has a particularly high FPG value and which subject has a particularly low FPG value relative to the pattern for the remaining subjects after the two outliers have been removed? Why?

 

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For this essay, describe the statistical approaches (e.g., identify the hypotheses and research methods) used in this excerpt from a research study.

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Statistics
Paper, Order, or Assignment Requirements

Part I: Essay Questions

Essay 1
Essay 2
Essay 3
Part II: Research Study Critique

Introduction
Methods
Results
Discussion
Your complete Word document must include a title page with the following:

Student’s name
Course name and number
Instructor’s name
Date submitted
Part I: Essay Questions
There are three essay questions in this section. You must answer all three questions. The length of each essay should be one to two double-spaced pages (excluding title and reference pages). Use 12-point font and format your paper with regular 1-inch margins. Do not include the essay prompt in your document. It will not count toward the length requirement for your essays.

Essay 1
A group of researchers conducted an experiment to determine which vaccine is more effective for preventing getting the flu. They tested two different types of vaccines: a shot and a nasal spray. To test the effectiveness, 1000 participants were randomly selected with 500 people getting the shot and 500 the nasal spray. Of the 500 people were treated with the shot, 80 developed the flu and 420 did not. Of the people who were treated with the nasal spray, 120 people developed the flu and 380 did not. The level of significance was set at .05. The proportion of people who were treated with the shot who developed the flu = .16, and the proportion of the people who were treated with the nasal spray was .24. The calculated p value = .0008.

For this essay, describe the statistical approaches (e.g., identify the hypotheses and research methods) used in this excerpt from a research study. Interpret the statistical results and examine the limitations of the statistical methods. Finally, evaluate the research study as a whole and apply what you have learned about hypothesis testing and inferential statistics by discussing how you might conduct a follow-up study.

Your essay must address the following points:

Describe the research question for this experiment.
What were the null and alternative hypotheses?
Were the results of this test statistically significant?
If so, why were they significant?
Would the researchers reject or fail to reject the null hypothesis?
Do the results provide sufficient evidence to support the alternative hypothesis?
Was the sample appropriate for this study? Explain your answer.
What are some possible limitations to this study?
Discuss how you would conduct a follow up study to this one. Explain your answer.
Describe the difference between practical and statistical significance.
Essay 2
A researcher has investigated the relationship between IQ and grade point average (GPA) and found the correlation to be .75.

For this essay, critique the results and interpretation of a correlational study.

Evaluate the correlational result and identify the strength of the correlation.
Examine the assumptions and limitations of the possible connection between the researcher’s chosen variables.
Identify and describe other statistical tests that could be used to study this relationship.
Your essay response must address the following questions:

How strong is this correlation?
Is this a positive or negative correlation?
What does this correlation mean?
Does this correlation imply that individuals with high Intelligence Quotients (IQ) have high Grade Point Averages (GPA)?
Does this correlation provide evidence that high IQ causes GPA to go higher?
What other variables might be influencing this relationship?
What is the connection between correlation and causation?
What are some of the factors that affect the size of this correlation?
Is correlation a good test for predicting GPA?
If not, what statistical tests should a researcher use, and why?
Essay 3
A researcher has recorded the reaction times of 20 individuals on a memory assessment. The following table indicates the individual times:

Will upload this table

In this essay, demonstrate your ability to organize data into meaningful sets, calculate basic descriptive statistics, interpret the results, and evaluate the effects of outliers and changes in the variables. You may use Excel, one of the many free online descriptive statistics calculators, or calculate the values by hand and/or with a calculator.

Next, separate the data into two groups of 10; one group will be the lower reaction times, and the second group will be the higher reaction times. Then, address the following points in your essay response:

Calculate the sum, mean, mode, median, standard deviation, range, skew, and kurtosis for each group.
How do the two groups differ?
Are there any outliers in either data group?
What effect does an outlier have on a sample?
Lastly, double each sample by repeating the same 10 data points in each group. You will have a total of 20 data points for each group. After completing this, address the following in your essay response:

Calculate the following for the new data groups: sum, mean, mode, median, standard deviation, range, skew, and kurtosis.
Did any of the values change?
How does sample size affect those values?
Part B: Research Study Critique
In this second portion of the Final Exam, you will identify and critically evaluate a quantitative research article based on a social science topic. Your selected article must include a research question(s) and/or hypothesis(es) and utilize statistical analyses covered in the course. The article must be peer-reviewed and published within the last 10 years.

In the body of your critique, describe the statistical approaches used, the variables included, the hypothesis(es) proposed, and the interpretation of the results. In your conclusion, suggest other statistical approaches that could have been used and, if appropriate, suggest alternative interpretations of the results. This process will allow you to apply the concepts learned throughout the course in the interpretation of actual scientific research. Your critique must include the following sections:

Introduction: This section will include a general introduction of the quantitative study from a peer-reviewed source published within the last 10 years. The research questions and/or hypothesis(es) as well as the purpose of the study should be clearly defined.
Methods: Describe and evaluate the procedures and methods of data collection, measures/instruments used, the participants and how they were selected, and the statistical techniques used.
Results: In this section describe and critique the results presented in the study.
Discussion: Discuss and evaluate the efficacy of the results presented in the study. Address, the strengths, weaknesses, and limitations of the study, and suggest future research directions. Include additional forms of statistical analyses as part of the suggestions for future research.
The Research Study Critique:

Must be three to four double-spaced pages in length (excluding title and reference pages) and formatted according to APA style as outlined in the Ashford Writing Center. Use 12-point font, with 1-inch margins.
Must use the sections and headings described above.
Must address the article with critical thought by examining, reflecting, and evaluating the article from an objective viewpoint and by using facts to support your argument. Refer to the Critical Thinking Community website for further assistance.
Must end with a conclusion that summarizes your critical evaluation.
Must use one quantitative research study from a peer-reviewed source that was published within the last 10 years.
Must properly cite the source article in APA style as outlined in the Ashford Writing Center.
Must include a separate reference page, formatted according to APA style as outlined in the Ashford Writing Center.

 

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Calculate (in units of 1000 books) the expected demand for the book, and the standard deviation of this demand.

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Math and statistics for business
Paper, Order, or Assignment Requirements

A new book is to be launched by a publishing firm to catch the Christmas market. The
manager of the firm wants to know how many books to print for this time-limited market. If
she prints too few, she will miss the opportunity for profit. If she prints too many, she will
have a lot of books left over in the New Year which will have to be sold off at a loss.
Suppose every book sold before Christmas makes a profit of £15 whilst the publishing firm
loses £5 for every book left over after Christmas. The pre-Christmas demand for the book
has a probability distribution given in the table below.
(i) Calculate (in units of 1000 books) the expected demand for the book, and the
standard deviation of this demand. [25 marks]
(ii) Calculate figures for a third column to the table, equalling the profit (in units of
£1,000) for each amount sold if the print run is 23,000 books. What is the return
(expected profit) in this case? [Note that (a) even if the demand is greater than
23,000, only 23,000 books will be sold; (b) when the demand is less than 23,000,
unsold books will have a negative impact on profits.] [25 marks]
(iii) By repeating (ii) for different print run sizes, calculate the print run size that will
maximise the expected profit. What is the risk (standard deviation) associated with
this strategy? Support your answers by calculating expected profit figures for each
possible stock level in a table.

 

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Calculate the descriptive statistics from the data and display in a table. Be sure to comment on the central tendency, variability and shape for each variable.

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Business Statistics Annual Number of Admissions to the Movies
Paper, Order, or Assignment Requirements

Answer all Questions

This assignment requires the use of Microsoft Excel. If you have Windows, you will also need to use the Data Analysis ToolPak. If you have a Mac with Excel 2011, you will need to use StatPlus:MAC LE.

Problem Description:

The following data correspond to the annual number of admissions (in millions) to the movies in Australia over the years 1994 and 2014. It also contains the yearly totas of the number of screens, theatres and flims screened, as well as the top price paid for a cinema ticket.

You will use descriptive statistics, inferential statistics and your knowledge of multiple linear regression to complete this task.

Admissions (Dependent Variable) and several characteristics (Independent Variables) are given in the Excel file: Tuesday.xlsx.

Here is a table describing the variables in the data set:

Variable Definition
Admissions (millions) Ticket admission to movie theatres in millions of customers
Screens Number of theatre screens available in Australia
Theatres Number of theatres open in Australia
Films Screened Number of films screened in Australia
Top Price Top Price of theatre ticket in Australia in 2014 $
Capacity Daily Capacity of customers in 000s.

Required:

Calculate the descriptive statistics from the data and display in a table. Be sure to comment on the central tendency, variability and shape for each variable. (1 Mark)
Draw a graph that displays the distribution of admissions. (1 Mark)
Create a box-and-whisker plot for the distribution of the top price and describe the shape. Is there evidence of outliers in the data? (1 Mark)
What is the likelihood that the admissions are greater than 70 million if the real price of tickets exceeds $20.00? Are admissions statistically independent of price? Use a Contingency Table. (2 Marks)
Estimate the 95% confidence interval for the population mean theatre capacity. (1 Mark)
Your supervisor recently stated that theatre admissions from 2008 through 2014 (ie. last 8 years) have exceeded the admissions in Taiwan which have been a constant 84 million per year. Test her claim at the 5% level of significance. (1 Mark)
Run a multiple linear regression using the data and show the output from Excel. (1 Mark)
Is the coefficient estimate for the real ticket price in 2014 $ different than zero at the 5% level of significance? Set-up the correct hypothesis test using the results found in the table in Part (G) using both the critical value and p-value approach. Interpret the coefficient estimate of the slope. (2 Marks)
Interpret the remaining slope coefficient estimates. Comment on whether the signs are what you are expecting. (2 Marks)
Interpret the value of the Adjusted R2. Is the overall model statistically significant at the 5% level of significance? Use the p-value approach. (1 Mark)
Do the results suggest that the data satisfy the assumptions of a linear regression: Linearity, Normality of the Errors, and Homoscedasticity of Errors? Show using scatter diagrams, normal probability plots and/or histograms and Explain. (3 Marks)
Based on the results of the regressions, is it likely that other factors have influenced the theatre admissions? If so, provide a couple possible examples and indicate whether these would likely influence the regression results if they were included. (1 Mark)
If a community housing organisation asked for information regarding the characteristics of housing targeting the households of native born Australians, explain whether a simple random sampling technique would provide an accurate representation of these households. (Note: This question does not use the data) (1 Mark)

 

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