Modular 2

Ch 1.3 to 1.5 Sampling

Ch 2.1 Organizing Qualitative Data Ch 1.3 to 1.5 Sampling Objective A : Ch 1.3 Simple Random Sampling Objective B : Ch 1.4 More Sampling Methods Objective C : Ch 1.5 Bias in Sampling Ch 2.1 Organizing Qualitative Data Objective A : Interpretation of a Basic Statistical Graph Objective B : Construct a Frequency / Relative Frequency Distribution, Bar Graph, Pareto Chart and Pie Chart Objective C : StatCrunch

Ch 1.3 to 1.5 Sampling Objective A : Ch 1.3 Simple Random Sampling The goal of sampling is to obtain as much information as possible about the population at the least cost. A random sample is obtained by using chance methods or random numbers. Example : Selecting a card from a well shuffled deck of cards.

Steps for Obtaining a Simple Random Sample 1. Number all the individuals in the population of interest. 2. Use a random number table, graphing calculator, or statistical software to randomly generate numbers where is the desired sample size.

Ch 2.1 Organizing Qualitative Data Ch 1.3 to 1.6 Sampling Objective A : Ch 1.3 Simple Random Sampling Objective B : Ch 1.4 More Sampling Methods Objective C : Ch 1.5 Bias in Sampling Ch 2.1 Organizing Qualitative Data Objective A : Interpretation of a Basic Statistical Graph Objective B : Construct a Frequency / Relative Frequency Distribution, Bar Graph, Pareto Chart and Pie Chart Objective C : StatCrunch

Objective B : Ch 1.4 More Sampling Methods A systematic sample is obtained by selecting every th individual from the population. A stratified sample is obtained by dividing the population into non- overlapping groups (called strata) according to some similar characteristic, then sampling from each stratum. A cluster is obtained by dividing the population into groups called the clusters such as geographic area or schools in a large district. Then all the individuals within a randomly selected clusters are selected. A convenience sample is a sample in which the individuals are easily obtained and not based on randomness.

Example 1: Identify the type of sampling method. (Random, systematic, stratified, cluster, convenience) (a) Every tenth customer entering a grocery store is asked to select her or his favor color. Systematic (b) A farmer divides his orchard into 30 subsections, randomly selects 4, and sample all the trees within the 4 subsections to approximate the yield of his orchard. Cluster (c) A survey regarding download time on a certain website is administered on the Internet by a market research firm to anyone who would like to take it. Convenience

(d) In an effort to identify is an advertising campaign has been effective, a marketing firm conducts a nationwide poll by randomly selecting individuals from a list of known users of the product. Random (e) A school official divides the student population into five classes: freshman, sophomore, junior, senior, and graduate student. The official takes a simple random sample from each class and asks the members’ opinions regarding student services. Stratified

Ch 2.1 Organizing Qualitative Data Ch 1.3 to 1.5 Sampling Objective A : Ch 1.3 Simple Random Sampling Objective B : Ch 1.4 More Sampling Methods Objective C : Ch 1.5 Bias in Sampling Ch 2.1 Organizing Qualitative Data Objective A : Interpretation of a Basic Statistical Graph Objective B : Construct a Frequency / Relative Frequency Distribution, Bar Graph, Pareto Chart and Pie Chart Objective C : StatCrunch

Ch 1.3 to 1.5 Sampling Objective C : Ch1.5 Bias in Sampling Sampling bias means that the technique used to obtain the individuals to be in the sample tends to favor one part of the population over another. Non-response bias exists when individuals selected to be in the sample do not wish to respond. Response bias exists when the answers on the survey do not reflect the true feelings of the respondent.

Example 1: The survey has bias. Determine the type of bias. (Sampling , non-response, response) (a) To determine the public’s opinion of the police department, the police chief obtains a cluster sample of 15 census tracts within his jurisdiction and samples all households in the randomly selected tracts. Uniformed police officers go door to door to conduct the survey. Response bias (b) The village of Oak Lawn wishes to conduct a study regarding the income level of households within the village. The village manager selects 10 homes in the southwest corner of the village and sends an interviewer to the homes to determine household income. Sampling bias

Ch 2.1 Organizing Qualitative Data Ch 1.3 to 1.5 Sampling Objective A : Ch 1.3 Simple Random Sampling Objective B : Ch 1.4 More Sampling Methods Objective C : Ch 1.5 Bias in Sampling Ch 2.1 Organizing Qualitative Data Objective A : Interpretation of a Basic Statistical Graph Objective B : Construct a Frequency / Relative Frequency Distribution, Bar Graph, Pareto Chart and Pie Chart Objective C : StatCrunch

Ch 2.1 Organizing Qualitative Data Objective A : Interpretation of a Basic Statistical Graph Example 1 : Identity Theft Identity fraud occurs someone else’s personal information is used to open credit card accounts, apply for a job, receive benefits, and so on. The following relative frequency bar graph represents the various types of identity theft based on a study conducted by the Federal Trade Commission.

(a) Approximate what percentage of identity theft was loan fraud (such as applying for a loan in someone else’s name)? (b) If there were 10 million cases of identity fraud in 2008, how many were credit card fraud (someone uses someone else’s credit card to make a purchase) ?

Ch 2.1 Organizing Qualitative Data Ch 1.3 to 1.6 Sampling Objective A : Ch 1.3 Simple Random Sampling Objective B : Ch 1.4 More Sampling Methods Objective C : Ch 1.5 Bias in Sampling Ch 2.1 Organizing Qualitative Data Objective A : Interpretation of a Basic Statistical Graph Objective B : Construct a Frequency / Relative Frequency Distribution, Bar Graph, Pareto Chart and Pie Chart Objective C : StatCrunch

Ch 2.1 Organizing Qualitative Data Objective B : Construct a Frequency / Relative Frequency Distribution, Bar Graph, Pareto Chart and Pie Chart B1. Frequency / Relative Frequency Distribution A frequency distribution lists each category of data and the frequency which is the number of occurrences for each category data. A relative frequency distribution lists each category of data and the relative frequency which is the proportion of observation within a category.

Example 1 : In a national survey conducted by the Centers of Disease Control to determine health-risk behaviors among college students, college students were asked, “How often do you wear a seat beat when driving a car?” The frequencies were as follows:

(a) Construct a relative frequency distribution.

(b) What percentage of respondents answered “Always”? 65% (c) What percentage of respondents answered “Never” or “Rarely”? 2% + 5% = 7% (d) Suppose that a representative from the Centers for Disease Control says, “2.5% of the college students in this survey responded that they never wear a seat belt.” Is this a descriptive or inferential statement? Descriptive statement.

Ch 2.1 Organizing Qualitative Data Objective B : Construct a Frequency / Relative Frequency Distribution, Bar Graph, Pareto Chart and Pie Chart B2. Construct a Bar Graph, a Pareto Chart, or a Pie Chart A bar graph is constructed by labeling each category of data on either the horizontal or vertical axis and the frequency or relative frequency of the category on the other axis. Rectangles of equal width are drawn for each category. The height of each rectangle represents the category’s frequency or relative frequency. A Pareto chart is a bar graph whose bars are drawn in decreasing order of frequency or relative frequency. A pie chart is a circle divided into sectors. Each sector represents a category of data. The area of each sector is proportion to the frequency of the category.

Example 2 : A sample of 40 randomly selected registered voters in Sylmar was asked their Political affiliation: Democrat (D), Republican (R), Independent (I). The results of the survey are as follows: R D R D R R D R D D D D R R D R D D I D D R R D D D I D R D D D I R D R D D D R (a) Construct a frequency distribution of the data.

(b) Construct a relative frequency distribution of the data. (c) Construct a frequency bar graph.

(d) Construct a relative frequency bar graph. (e) Construct a Pareto chart.

(f) Construct a pie chart.

Ch 2.1 Organizing Qualitative Data Ch 1.3 to 1.6 Sampling Objective A : Ch 1.3 Simple Random Sampling Objective B : Ch 1.4 More Sampling Methods Objective C : Ch 1.5 Bias in Sampling Ch 2.1 Organizing Qualitative Data Objective A : Interpretation of a Basic Statistical Graph Objective B : Construct a Frequency / Relative Frequency Distribution, Bar Graph, Pareto Chart and Pie Chart Objective C : StatCrunch