Workbook for stats with practice questions PDF

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Practice questions for stats, great for studying...

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IIE Module Guide

BSTA6212

BUSINESS STATISTICS WORKBOOK 2021

This manual enjoys copyright under the Berne Convention. In terms of the Copyright Act, no 98 of 1978, no part of this manual may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording or by any other information storage and retrieval system without permission in writing from the proprietor.

The Independent Institute of Education (Pty) Ltd is registered with the Department of Higher Education and Training as a private higher education institution under the Higher Education Act, 1997 (reg. no. 2007/HE07/002). Company registration number: 1987/004754/07.

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DID YOU KNOW? Student Portal The full-service Student Portal provides you with access to your academic administrative information, including: • an online calendar, • timetable, • academic results, • module content, • financial account, and so much more!

Module Guides or Module Manuals When you log into the Student Portal, the ‘Module Information’ page displays the ‘Module Purpose’ and ‘Textbook Information’ including the online ‘Module Guides or ‘Module Manuals’ and assignments for each module for which you are registered.

Supplementary Materials For certain modules, electronic supplementary material is available to you via the ‘Supplementary Module Material’ link.

Module Discussion Forum The ‘Module Discussion Forum’ may be used by your lecturer to discuss any topics with you related to any supplementary materials and activities such as ICE, etc. To view, print and annotate these related PDF documents, download Adobe Reader at following link below: www.adobe.com/products/reader.html

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IIE Library Online Databases The following Library Online Databases are available to you. Please contact your librarian if you are unable to access any of these. Use the same username and password as for student portal Library Website

This library website gives access to various online resources and study support guides [Link]

LibraryConnect (OPAC)

The Online Public Access Catalogue. Here you will be able to search for books that are available in all the IIE campus libraries. [Link]

EBSCOhost

This database contains full text online articles. [Link]

EBSCO eBook Collection

This database contains full text online eBooks. [Link]

SABINET

This database will provide you with books available in other libraries across South Africa. [Link]

DOAJ

DOAJ is an online directory that indexes and provides access to high quality, open access, peer-reviewed journals. [Link]

DOAB

Directory of open access books. [Link]

IIESPACE

The IIE open access research repository [Link]

Emerald

Emerald Insight [Link]

HeinOnline

Law database [Link]

JutaStat

Law database [Link]

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Table of Contents Using this Workbook ................................................................................................. 5 Learning Unit 1: Introduction To Statistics ................................................................. 6 1. Activities ............................................................................................................ 6 2. Revision Exercises .......................................................................................... 11 3. Solutions To Activities And Revision Exercises................................................ 17 Learning Unit 2: Descriptive Statistics ..................................................................... 24 1. Activities .......................................................................................................... 24 2. Revision Exercises .......................................................................................... 30 3 Solutions To Activities And Revision Exercises................................................ 37 Learning Unit 3: Basic Probability ............................................................................ 52 1 Activities .......................................................................................................... 52 2 Revision Exercises .......................................................................................... 58 3 Solutions To Activities And Revision Exercises................................................ 62 Learning Unit 4: Probability Distributions ................................................................. 68 1 Activities .......................................................................................................... 68 2 Revision Exercises .......................................................................................... 71 3 Solutions to Activities And Revision Exercises ................................................. 75 Learning Unit 5: Introduction To Sampling Distributions .......................................... 81 1 Activities .......................................................................................................... 81 2 Revision Exercises .......................................................................................... 83 3 Solutions To Activities And Revision Exercises................................................ 85 Learning Unit 6: Hypothesis Testing ........................................................................ 88 1 Activities .......................................................................................................... 88 2. Revision Exercises .......................................................................................... 90 3. Solutions to Exercises ..................................................................................... 91 Learning Unit 7: Chi-Square Tests .......................................................................... 96 1 Activities .......................................................................................................... 96 2 Revision Exercises .........................................................................................100 3 Solutions To Activities And Revision Exercises...............................................102 Learning Unit 8: Linear Regression And Correlation Analysis .................................111 1 Activities .........................................................................................................117 2 Revision Exercises .........................................................................................119 3 Solutions To Activities And Revision Exercises...............................................122 Learning Unit 9: Index Numbers .............................................................................127 1 Activities .........................................................................................................127 2 Revision Exercises .........................................................................................130 3. Solutions To Activities And Revision Exercises...............................................132 Formula Sheet - Quantitative Techniques (QUAT6221) .........................................139 Bibliography ...........................................................................................................144

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Using this Workbook This workbook has been developed to support your use of the prescribed material for this module. Various activities and revision questions are designed to help you to engage with the subject matter as well as to help you prepare for your assessments.

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Learning Unit 1: Introduction to Statistics Material used for this Learning Unit: •

Prescribed Textbook, Chapter One.

1. Activities 1.1 Activity 1 Purpose: The purpose of this activity is to distinguish between statistical concept antonyms. Task: 1.

2.

Identify the population and the sample in each of the following situations: 1.1

50 smokers were selected at random to determine what the effectiveness of a televised anti-smoking campaign is on smokers.

1.2

A very popular radio station selected 200 people at random to determine listeners’ attitudes towards certain programmes broadcast during the day.

1.3

In a recent survey, 3 000 South Africans were asked if they read the newspaper daily; 600 said ‘Yes’.

The purpose of the following is to assist students in identifying primary and/or secondary data: 2.1

Will information obtained to determine the water levels of the major storage dams in South Africa be primary or secondary data? Where can this data be obtained from?

2.2

Describe how you would go about determining the number of filling stations in your area, using both a secondary source and a primary source.

2.3

Identify a problem where you can make use of secondary data.

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2.4

3.

4.

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Identify a problem where you can make use of primary data.

For each of the following situations, would you recommend taking a sample or performing a census? Explain your reasoning in each instance: 3.1

A jeweller just received a delivery of shockresistant watches, and wishes to determine (approximately) the greatest height from which the watches can be dropped onto a concrete surface without breaking the crystal.

3.2

Tiger Mills wishes to determine the age, gender and income characteristics of people who consume Cheerio breakfast cereal.

3.3

The producers of the Early Bird show want to find out what percentage of television (TV) viewers recognise a photo of host, Joseph Khumalo.

3.4

A researcher wishes to determine whether companies that manufacture nuclear submarines would be interested in a new technique for purifying air when such craft are submerged.

In the following examples, determine whether we are dealing with a parameter or a statistic: 4.1

When surveying the political choices of voters, a sample of voters is selected from the population of all eligible voters. Based on the results observed for the sample statistics, the analyst then makes inferences regarding the political choices that are likely to exist in the population of voters.

4.2

A recent survey of a sample of graduates reported that the average starting salary for a graduate is less than R30 000 per year.

4.3

Starting salaries for 270 graduates increased by 5% from the previous year.

4.4

In a random check of a sample of retail stores, the local health inspector found that 24% of the stores were not storing fish at the proper temperature.

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4.5

5.

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In 2004, all major league soccer teams spent a total of R1 968 088 on players’ salaries. Decide whether the numerical value is from a population or a sample, and then specify whether it is a parameter or a statistic.

Indicate whether the corresponding sets of observations would be quantitative or qualitative. If quantitative, distinguish between discrete and continuous. Quantitative

Qualitative

Discrete

Continuous

Ethnic group Age ID number Net worth (rand) Favourite sport Temperature Home language Cooking time for pasta Speed of an aeroplane Gender

Activity 2 Purpose: The purpose of this activity is to identify the measurement scale associated with different variables. Task: Specify the measurement scale for each of the following: 1.

Whether you are a South African (SA) citizen.

2.

The amount you paid to fill up your petrol tank.

3.

The time it took you to get to the university this morning.

4.

The size of your take-away coffee.

5.

Your belt size.

6.

Your student number.

7.

The occupation of 200 shoppers at a supermarket.

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8.

The daily temperature measured inside the supermarket.

9.

The amount spent by every shopper at a supermarket.

10.

Rating a new product as good, average or poor.

11.

The recording of the first three digits of the shoppers’ cell phone numbers.

BSTA6212

Commentary related to this activity: When dealing with measures of description, only certain descriptive measures can be used with certain measurement scales of data.

Activity 3 Purpose: The purpose of this activity is to analyse a case study in terms of the basic statistical concepts. Task: The South African government is concerned about the high illiteracy rates amongst adults in South Africa. They wish to estimate the true proportion of adults (over 18 years of age) in South Africa who are illiterate (that is, that cannot read or write in at least one language). A random sample of 10 000 adults were interviewed, and 1 107 of them were found to be illiterate. 1.

The sample space is __________________?

2.

The parameter of interest is __________________?

3.

The statistic is __________________?

4.

The sample size is __________________?

5.

The population size is __________________?

6.

The variable is __________________?

7.

The measurement scale of the variable is ___________?

8.

The type of data is __________________?

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Commentary related to this activity: Competency in this activity means that you have developed a good understanding of some important statistical concepts.

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2. Revision Exercises 2.1 Revision Exercise 1 1.

Classify the following sets of data as qualitative or quantitative. If classified as quantitative, is it discrete or continuous? Quantitative

Qualitative

Discrete

Continuous

The weight of each member of a soccer team Religious affiliation Marks obtained in 1st test The colours you can identify in a rainbow Telephone numbers in a telephone directory The number of sit-ups you can do The daily temperature at 12h00 Number of traffic fatalities Time required to complete a crossword puzzle The ages of the students in your study group

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2.

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What is the measurement scale for each of the given variables?

Religious affiliation The number of sit-ups you can do The daily temperature at 12h00 Number of traffic fatalities Time required to complete a crossword puzzle The ages of the students in your study group The colours you can identify in a rainbow Telephone numbers in a telephone directory Shoe sizes The three major professional tennis tournaments listed: Australian Open; Wimbledon; US Open The amount of weight lost in the past month by a person following a strict diet The classification of Boeing aircraft as 727, 737 or 747, according to size 3.

A recent study on the average amount of time spent watching TV per day by a group of students yielded the following results:

Academic Status 1st years 2nd years 3rd years

Number of Students 30 20 10

Average Time (Hours) Spent Watching TV 6.4 4.5 2.8

Choose the correct word in each of the following statements: The 60 students involved in the study constitute a sample/population of students. The figure 6.4 is a parameter/statistic. The estimate of the average amount of time spent watching TV per week by all 1st year students involves a descriptive/inferential technique. The variable of interest is the number of students/average time watching TV. The average times calculated for the three groups of students are of a discrete/continuous nature. The academic status of the students can be classified as quantitative/qualitative data.

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2.2 Revision Exercise 2 1.

The collection of all possible individuals, objects or measurements is known as: 1.1 1.2 1.3 1.4

2.

Techniques used to organise, summarise, and present the data that has been collected are known as: 2.1 2.2 2.3 2.4

3.

A chance of being selected; The same chance of being selected; A 50% chance of being selected; No chance of being selected.

The sample mean is an example of a _____________. 5.1 5.2 5.3 5.4

6.

Populations; Samples; Inferential statistics; Descriptive statistics.

In a random sample, each item in the population has: 4.1 4.2 4.3 4.4

5.

Populations; Samples; Inferential statistics; Descriptive statistics.

Techniques used to estimate a population parameter, based on a sample, are known as: 3.1 3.2 3.3 3.4

4.

A sample; A population; An inference; A statistic.

Sample statistic; Population parameter; Measurement scale; Discrete variable.

Primary data is collected by: 6.1 6.2 6.3 6.4

Primary school children; People collecting it for the first time; The actual people who will be using it; Mainly experienced people.

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7.

Secondary data are obtained from: 7.1 7.2 7.3 7.4

8.

Simple random sampling method; Systematic random sampling method; Stratified random sampling method; Snowball sampling method.

Once every hour, a random sample of 12 light bulbs is selected from an assembly line delivering this type of light bulb. The number of bulbs in each sample that will not light is divided by 12 to obtain the defective proportion. What is the variable? 10.1 10.2 10.3 10.4

11.

Sampling; Using a secondary source; Asking questions; Using the random number table.

To estimate the percentage of defects in a recent manufacturing batch, the quality control manager of Intel Computers selects every 8th chip that comes off the as...