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## Statistics Assignment

•Business Analytics

•Chapter 1

What is Statistics?
•Chapter outline

1.1 Key statistical concepts1.2 Practical applications

1.3 How managers use statistics

1.4 Online resources

•Learning objectives

LO1 describe the two major branches of statistics – descriptive statistics and inferential statisticsLO2 understand the key statistical concepts – population, sample, parameter, statistic and census

LO3 provide examples of practical applications in which statistics have a major role to play

LO4 understand the basics of the computer spreadsheet package Microsoft excel and its capabilities in aiding with statistical data analysis for large amounts of data.

•Introduction to Statistics

In today’s world we have access to more data than ever.For example, data are collected for business applications from:

•Direct observation or measurement

•Customer surveys

•Political polls

•Economic surveys

•Marketing surveys

This chapter introduces various statistical concepts. In Chapter 2, we introduce various methods of data collection.

•In today’s world…

How can we make use of the collected data to help make informed business decisions?By learning statistics, which is a collection of various techniques and tools, we can help make such decisions.

•What is Statistics?

‘Statistics is a body of principles and methods concerned with extracting useful information from a set of data to help people make informed business decisions.’
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•What is Statistics?

‘Statistics is a way to get informationfrom data to make informed decisions.’

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•Two major branches of Statistics

1.Descriptive Statistics

2.Inferential Statistics

•Descriptive Statistics

Descriptive statistics deals with methods of organising, summarising, and presenting data in a convenient and informative way.One form of descriptive statistics uses graphical techniques, which allow statistics practitioners to present data in ways that make it easy for the reader to extract useful information.

Chapters 3 and 4 introduce several graphical methods.

•Descriptive Statistics

Another form of descriptive statistics uses numerical measures to summarise data.The mean and median are popular numerical measures to describe the location of the data.

The range, variance and standard deviation measure the variability of the data

Chapter 5 introduces several numerical statistical measures that describe different features of the data.

•Inferential Statistics

Descriptive statistics describe the data set that is being analysed, but does not provide any tools for us to draw any conclusions or make any inferences about the data. Hence we need another branch of statistics: inferential statistics.Inferential statistics is also a set of methods, but it is used to draw conclusions or inferences about characteristics of populations based on sample statistics calculated from sample data.

Chapters 9-22 introduce several techniques in inferential statistics.

•1.1 Key Statistical concepts

PopulationA population is the group of

__all__items (data) of interest.

Population is frequently very large; sometimes infinite.

E.g. 1. All current million or so members of an automobile club (Example 1.3).

2. All prawns available at the freshwater prawn Farm A in Queensland.

•Key statistical concepts

SampleA sample is a set of items (data) drawn from the population of interest.

Sample could potentially be very large, but much less than the population.

E.g. 1. A sample of 500 members of the automobile club selected.

2. A sample of 1000 prawns selected from different sections of the freshwater prawn Farm A.

•Key statistical concepts

ParameterA descriptive measure of a population.

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StatisticA descriptive measure of a sample.

•Key statistical concepts

A descriptive measure of a population is called a parameter (e.g. Population mean)A descriptive measure of a sample is called a statistic (e.g. Sample mean)

•Statistical Inference

Statistical inference is the process of making an estimate, prediction, or decision about a population based on a sample.
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•Statistical Inference

We use sample statistics to make inferences about population parameters.Therefore, we can produce an estimate, prediction, or decision about a population based on sample data.

Thus, we can apply what we know about a sample to the larger population from which it was drawn!

•Statistical inference

__Rationale:__

•Large populations make investigating each member impractical and expensive.

•Easier and cheaper to take a sample and make estimates about the population from the sample.

__However:__

•Such conclusions and estimates are not always going to be correct.

•For this reason, we build into the statistical inference ‘measures of reliability’, namely confidence level and significance level.

•Confidence and Significance Levels

When the purpose of the statistical inference is to draw a conclusion about a population, the significance level measures how frequently the conclusion will be wrong in the long run.For example, a 5% significance level means that, in the long run, this type of conclusion will be wrong 5% of the time.

•Confidence and Significance Levels

The confidence level is the proportion of times that an estimating procedure will be correct.For example, a confidence level of 95% means that, estimates based on this form of statistical inference will be correct 95% of the time.

•Confidence and Significance Levels

Consider a statement from polling data you may hear about in the news:‘This poll is considered accurate within

3.4 percentage points, 19 times out of 20.’

In this case, our confidence level is 95% (19/20 = 0.95), while our significance level is 5%.

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•1.2 Practical applications

Example 1: Pepsi’s Exclusivity AgreementA large university with a total enrolment of about 50,000 students has offered Pepsi-Cola an exclusivity agreement that would give Pepsi exclusive rights to sell its products at all university facilities for the next year with an option for future years. In return, the university would receive 35% of the on-campus revenues and an additional lump sum of $200,000 per year.

Pepsi has been given 2 weeks to respond.

•Example 1: Pepsi’s Exclusivity Agreement

The market for soft drinks is measured in terms of 375ml cans. Pepsi currently sells an average of 10,000 cans per week (over the 30 weeks of the year during two teaching semesters that the university operates). The problem is that we do not know how many soft drinks (all types including Pepsi) are sold weekly at the university (this information is needed to calculate total profit from the deal)
•What is the population of interest in this case?

•The cost of interviewing each student is too high and extremely time consuming. It is therefore not possible to interview every student. What is the best way to get an estimate of the total soft drinks consumption sold at the university?

•Example 1: Solution

What is the population of interest in this case?
•the soft drink consumption of the university’s 50 000 students.

What is the best way to get an estimate of the total soft drinks consumption sold at the university?

•we can sample a much smaller number of students (the sample size is 500) and infer from the sample data the number of soft drinks consumed by all 50,000 students.

•Example 1:Pepsi’s Exclusivity Agreement

Suppose Pepsi assigned you to survey a sample of 500 students to infer from the sample data the number of soft drinks consumed by all 50,000 students. Accordingly, you organise a survey that asks 500 students to keep track of the number of soft drinks by type of drink (Pepsi, Coke, Lemonade etc.) they purchase during the next 7 days.Discuss how would Pepsi use the data collected by you to get estimates of the soft drink consumption?

•Example 1: Solution

The answer to his question involves inferential statistics.Since revenue generated from the consumption of each soft drink is equal to

(price of the soft drink) x (mean consumption) x 50,0000

Since, mean consumption (consumption per student) of the population is not known, using our insight from inferential statistics we can get an estimate of the mean consumption from the sample data (500 students).

•More Examples

You will see many examples of practical applications through out this subject. Almost all lectures and tutorials will cover practical applications.
•1.3 How managers use statistics

Statistical Applications in BusinessStatistical analysis plays an important role in virtually all aspects of business and economics.

Throughout this course, we will see applications of statistics in accounting, economics, finance, human resources management, marketing, and operations management.

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