Welcome to QM Business Statistics

Course Objectives: Again 1.To gain an understanding of descriptive statistics, probability, sampling, interval estimation, hypothesis testing, and linear regression. 2.To perform applications of statistical methods to business problems using the spreadsheet software Excel.

Some statistics The top 3 makers of breakfast cereal account for 95 percent of domestic sales. The average price of a movie ticket is $5.60. The dollar has lost 35 percent of its value against the euro since percent of New York City students dropped out of school in academic year Industrial production in China increased by 15.7 percent in E-commerce sites spend an average of $108 to acquire a new customer.

Statistics is the art and science of collecting, analyzing, presenting, and interpreting data.

Applications in Business & Economics Accounting: Auditing function, for example, relies on statistical sampling techniques. Finance: Portfolio managers use a variety of statistics, such as the price/earnings ratio, to determine if shares are properly valued by the market. Marketing: Market studies used for decision making about store or restaurant location, product lines or services sold, involve statistical analysis.

Applications in Business & Economics: Continued Production: Bottling plants use X-bar charts to prevent over or under filling—i.e., make sure that the average number of ounces falls within acceptable limits. Economics: Economists use statistical techniques to forecast important variables such as inflation or unemployment.

Elements, Variables, and Observations Elements are the entities on which data is collected. Variables are characteristics of interest for elements. Observations are the measurements for a particular element.

StudentHigh School HeightWeight RobertLincoln5’11”170 lbs. PortiaSouthside5’7”120 lbs. EdwardOak Ridge6’2”198 lbs. Students are the elements. High school, height and weight are the variables. 5’11”, 120 lbs, etc. are the observations.

Nominal and Ordinal Scales The scale of measurement for a variable is a nominal scale when the data are labels or names used to identify an attribute of the element. The scale of measurement is an ordinal scale if the order or rank of the data is meaningful.

StudentHigh School HeightWeight RobertLincoln5’11”170 lbs. PortiaSouthside5’7”120 lbs. EdwardOak Ridge6’2”198 lbs. The scale of measurement for the high school variable is nominal. Scales of measurement for the height and weight variables are ordinal.

Scales of Measurement The data have the properties of ordinal data, andThe data have the properties of ordinal data, and the interval between observations is expressed in the interval between observations is expressed in terms of a fixed unit of measure. terms of a fixed unit of measure. Interval data are always numeric.Interval data are always numeric. Interval Example: Example: Melissa has an SAT score of 1205, while Kevin Melissa has an SAT score of 1205, while Kevin has an SAT score of Melissa scored 115 has an SAT score of Melissa scored 115 points more than Kevin. points more than Kevin. Example: Example: Melissa has an SAT score of 1205, while Kevin Melissa has an SAT score of 1205, while Kevin has an SAT score of Melissa scored 115 has an SAT score of Melissa scored 115 points more than Kevin. points more than Kevin.

Scales of Measurement Ratio The data have all the properties of interval dataThe data have all the properties of interval data and the ratio of two values is meaningful. and the ratio of two values is meaningful. This scale must contain a zero value that indicatesThis scale must contain a zero value that indicates that nothing exists for the variable at the zero point that nothing exists for the variable at the zero point Example: Example: Melissa’s college record shows 36 credit hours Melissa’s college record shows 36 credit hours earned, while Kevin’s record shows 72 credit earned, while Kevin’s record shows 72 credit hours earned. Kevin has twice as many credit hours earned. Kevin has twice as many credit hours earned as Melissa. hours earned as Melissa. Example: Example: Melissa’s college record shows 36 credit hours Melissa’s college record shows 36 credit hours earned, while Kevin’s record shows 72 credit earned, while Kevin’s record shows 72 credit hours earned. Kevin has twice as many credit hours earned. Kevin has twice as many credit hours earned as Melissa. hours earned as Melissa.

Qualitative and Quantitative Data Qualitative, or categorical, data are labels or names used to identify an attribute of each element. Can be numeric or non-numeric. Quantitative data are numeric values indicating how much or how many.

StudentHigh School HeightWeight Robert15’11”170 lbs. Portia25’7”120 lbs. Edward36’2”198 lbs. High School remains a qualitative variable— even though we are now labeling it with numbers. Arithmetic operations for numeric qualitative variables are meaningless.

Scales of Measurement QualitativeQualitativeQuantitativeQuantitative NumericalNumerical NumericalNumerical NonnumericalNonnumerical DataData NominalNominalOrdinalOrdinalNominalNominalOrdinalOrdinalIntervalIntervalRatioRatio

Time -series data: historical data--i.e., the data sample consists of a series of daily, monthly, quarterly, or annual data for variables such as prices, income, employment, output, car sales, stock market indices, exchange rates, and so on. Cross-sectional data: All observations in the sample are taken from the same point in time and represent different individual entities (such as households, houses, etc.) Types of data

Time series data: Daily observations, Korean Won per dollar

Student IDSexAgeHeightWeight M216’1”178 lbs M285’11”205 lbs F195’8”121 lbs F225’4”98 lbs M206’2”183 lbs Example of cross sectional data

Time-series graph

Unemployment rates in industrialized countries, May 2000 Source: The Economist Cross- section graph

Descriptive Statistics Summaries of data that can be in tabular, graphical, or numerical form.

Example: Hudson Auto Repair The manager of Hudson Auto would like to have a better understanding of the cost of parts used in the engine tune-ups performed in the shop. She examines 50 customer invoices for tune-ups. The costs of parts, rounded to the nearest dollar, are listed on the next slide.

Example: Hudson Auto Repair Example: Hudson Auto Repair n Sample of Parts Cost for 50 Tune-ups

Tabular Summary: Frequency and Percent Frequency (2/50)100 Parts Cost ($) Parts Frequency Percent Frequency

Graphical Summary: Histogram Parts Cost ($) Parts Cost ($) Frequency Tune-up Parts Cost

Population Sample Statistical inference Census Sample survey  the set of all elements of interest in a particular study particular study  a subset of the population  the process of using data obtained from a sample to make estimates from a sample to make estimates and test hypotheses about the and test hypotheses about the characteristics of a population characteristics of a population  collecting data for a population  collecting data for a sample

The Process of Statistical Inference for the Norris Electronics Example 1. Population consists of all bulbs manufactured with the new filament. Average lifetime is unknown 2. A sample of 200 bulbs is manufactured with the new filament 3. The sample data provide a sample average lifetime of 76 hours per bulb 4. The sample average is Used to estimate the population Average.

The Sample Hours Until Burnout

Statistical Analysis Using Microsoft Excel 1.Enter the data in the Excel Spreadsheet 2.Enter functions and formulas 3.Apply tools