statistics exam

Data and Statistics Statistics (exercises)

Aleksandra Pawłowska

March 31, 2020

Glossary (part 1)

Statistics The art and science of collecting, analyzing, presenting, and interpret- ing data. Data The facts and figures collected, analyzed, and summarized for presentation and interpretation. Data set All the data collected in a particular study. Elements The entities on which data are collected. Variable A characteristic of interest for the elements. Observation The set of measurements obtained for a particular element. Nominal scale The scale of measurement for a variable when the data are labels or names used to identify an attribute of an element. Nominal data may be nonnumeric or numeric. Ordinal scale The scale of measurement for a variable if the data exhibit the properties of nominal data and the order or rank of the data is meaningful. Ordinal data may be nonnumeric or numeric. Interval scale The scale of measurement for a variable if the data demonstrate the properties of ordinal data and the interval between values is expressed in terms of a fixed unit of measure. Interval data are always numeric.

Aleksandra Pawłowska Data and Statistics

Glossary (part 2) Ratio scale The scale of measurement for a variable if the data demonstrate all the properties of interval data and the ratio of two values is meaningful. Ratio data are always numeric. Categorical data Labels or names used to identify an attribute of each element. Categorical data use either the nominal or ordinal scale of measurement and may be nonnumeric or numeric. Quantitative data Numeric values that indicate how much or how many of something. Quantitative data are obtained using either the interval or ratio scale of measurement. Categorical variable A variable with categorical data. Quantitative variable A variable with quantitative data. Cross-sectional data Data collected at the same or approximately the same point in time. Time series data Data collected over several time periods. Descriptive statistics Tabular, graphical, and numerical summaries of data. Population The set of all elements of interest in a particular study. Sample A subset of the population. Census A survey to collect data on the entire population. Sample survey A survey to collect data on a sample. Statistical inference The process of using data obtained from a sample to make estimates or test hypotheses about the characteristics of a population.

Aleksandra Pawłowska Data and Statistics

Useful tips

1 An observation is the set of measurements obtained for each element in a data set. Hence, the number of observations is always the same as the number of elements. The number of measurements obtained for each element equals the number of variables. Hence, the total number of data items can be determined by multiplying the number of observations by the number of variables.

2 Quantitative data may be discrete or continuous. Quantitative data that measure how many (e.g. number of calls received in 5 minutes) are discrete. Quantitative data that measure how much (e.g. weight or time) are continuous because no separation occurs between the possible data values.

Aleksandra Pawłowska Data and Statistics

Exercises

Aleksandra Pawłowska Data and Statistics

Task 1

The U.S. Department of Energy provides fuel economy information for a variety of motor vehicles. A sample of 10 automobiles is shown in Table 1.6 (Fuel Economy website, February 22, 2008). Data show the size of the automobile (compact, midsize, or large), the number of cylinders in the engine, the city driving miles per gallon, the highway driving miles per gallon, and the recommended fuel (diesel, premium, or regular).

1 How many elements are in this data set? 2 How many variables are in this data set? 3 Which variables are categorical and which variables are

quantitative? 4 What type of measurement scale is used for each of the

variables?

Aleksandra Pawłowska Data and Statistics

Task 2

Refer to Table 1.6. 1 What is the average miles per gallon for city driving? 2 On average, how much higher is the miles per gallon for

highway driving as compared to city driving? 3 What percentage of the cars have four-cylinder engines? 4 What percentage of the cars use regular fuel?

Aleksandra Pawłowska Data and Statistics

Aleksandra Pawłowska Data and Statistics

Task 3

Table 1.7 shows data for seven colleges and universities. The en- dowment (in billions of dollars) and the percentage of applicants admitted are shown (USA Today, February 3, 2008). The state each school is located in, the campus setting, and the NCAA Di- vision for varsity teams were obtained from the National Center of Education Statistics website, February 22, 2008.

1 How many elements are in the data set? 2 How many variables are in the data set? 3 Which of the variables are categorical and which are

quantitative?

Aleksandra Pawłowska Data and Statistics

Task 4

Consider the data set in Table 1.7 1 Compute the average endowment for the sample. 2 Compute the average percentage of applicants admitted. 3 What percentage of the schools have NCAA Division III

varsity teams? 4 What percentage of the schools have a City: Midsize campus

setting?

Aleksandra Pawłowska Data and Statistics

Task 5

The FinancialTimes/Harris Poll is a monthly online poll of adults from six countries in Europe and the United States. A January poll included 1015 adults in the United States. One of the questions asked was, “How would you rate the Federal Bank in handling the credit problems in the financial markets?” Possible responses were Excellent, Good, Fair, Bad, and Terrible (Harris Interactive website, January 2008).

1 What was the sample size for this survey? 2 Are the data categorical or quantitative? 3 Would it make more sense to use averages or percentages as a

summary of the data for this question? 4 Of the respondents in the United States, 10% said the Federal

Bank is doing a good job. How many individuals provided this response?

Aleksandra Pawłowska Data and Statistics

Task 6

The Commerce Department reported receiving the following appli- cations for the Malcolm Baldrige National Quality Award: 23 from large manufacturing firms, 18 from large service firms, and 30 from small businesses.

1 Is type of business a categorical or quantitative variable? 2 What percentage of the applications came from small

businesses?

Aleksandra Pawłowska Data and Statistics

Task 7

State whether each of the following variables is categorical or quan- titative and indicate its measurement scale.

1 Annual sales 2 Soft drink size (small, medium, large) 3 Employee classification (GS1 through GS18) 4 Earnings per share 5 Method of payment (cash, check, credit card)

Aleksandra Pawłowska Data and Statistics

Aleksandra Pawłowska Data and Statistics

Task 8

Figure 1.8 provides a bar chart showing the amount of federal spend- ing for the years 2002 to 2008 (USA Today, February 5, 2008).

1 What is the variable of interest? 2 Are the data categorical or quantitative? 3 Are the data time series or cross-sectional? 4 Comment on the trend in federal spending over time.

Aleksandra Pawłowska Data and Statistics

Aleksandra Pawłowska Data and Statistics

Task 9

The Food and Drug Administration (FDA) reported the number of new drugs approved over an eight-year period (The Wall Street Jour- nal, January 12, 2004). Figure 1.9 provides a bar chart summarizing the number of new drugs approved each year.

1 Are the data categorical or quantitative? 2 Are the data time series or cross-sectional? 3 How many new drugs were approved in 2003? 4 In what year were the fewest new drugs approved? How

many? 5 Comment on the trend in the number of new drugs approved

by the FDA over the eight-year period.

Aleksandra Pawłowska Data and Statistics

Task 10

Asample of midterm grades for five students showed the following results: 72, 65, 82, 90, 76. Which of the following statements are correct, and which should be challenged as being too generalized?

1 The average midterm grade for the sample of five students is 77.

2 The average midterm grade for all students who took the exam is 77.

3 An estimate of the average midterm grade for all students who took the exam is 77.

4 More than half of the students who take this exam will score between 70 and 85.

5 If five other students are included in the sample, their grades will be between 65 and 90.

Aleksandra Pawłowska Data and Statistics