Section Introduction

Transcription

1 Section Introduction Raw Data is data before it has been arranged in a useful manner or analyzed using statistical techniques. Statistics involves the procedures associated with the data collection process, the summarizing and interpretation of data, and the drawing of inferences or conclusions based upon the analysis of the data. Descriptive Statistics uses numerical and/or visual techniques to summarize or describe the data in a clear and effective manner. CASE STUDY 1.1 on pg. 2 in Text - NHL as a Growth Industry The snapshot entitled NHL a Growth Industry is shown in Figure 1.1 (see textbook pg. 3). This snapshot compares the size of the average NHL player of the season to the average NHL player of the season. The population is the entire collection of all individuals or objects of interest. What is the population in the above problem? The sample is the portion of the population that is selected for study. What could be a sample for the above problem? Inferential Statistics is the process of using sample information to draw inferences or conclusions about the population. What if a medical researcher wants to determine if large doses of vitamin C are effective in combating colds? A representative sample is a sample that has the pertinent characteristics of the population in the same proportion, as they are included in that population. A statistic is a number that describes a characteristic of a sample. A parameter is a number that describes a characteristic of a population. Example 1.1 on pg. 6 in Text A statistician computes the batting average of all American League players to be.285 and the batting average of 24 players randomly selected from all the American League players to be.267. If the population is defined to be all the baseball players in the American League, then determine which batting average represents a parameter and which one is a statistic? 1

2 Example 1.2 on pg. 7 in Text A politician is interested in determining the proportion of 20,000 voters within her district who will vote for her in the upcoming election. An opinion poll of 1500 potential voters was taken to estimate how all the voters in her district will vote in the upcoming election. The results of the opinion poll indicate that 52% will vote for the politician in the upcoming election. Determine: a. The population. b. The sample. c. Whether the result, 52%, is a parameter or statistic. Section Why Sample? Sampling is the process of selecting a portion, or sample, of the entire population. A survey that includes every item or individual of the population is called a census. Why Sample? Samples are taken when it is either impossible or impractical to examine the entire population. Studying an entire population is impractical when the population is extremely large. What if the quality control department at G.E. wants to test the production of its light bulbs to determine if they meet company specifications regarding the mean life of the bulbs? Sample Size The size of a sample, denoted by n, is the number of data values in the sample. Population Size The size of a finite population, denoted by N, is the number of data values in the population. Reasons for Sampling 1. A census is impossible 2. Cost 3. Time 4. Accuracy Section Sampling Techniques A simple random sample is a sample of data values selected from a population in such a way that every sample of size n has an equal probability of being selected and every data value of the population has the same chance of being selected for the sample. Selecting a non-representative or biased sample from a population can lead to invalid inferences about the population. 2

3 Example 1.3 on pg. 12 in Text Determine if each of the following sampling procedures will produce a random sample. a. The population is all females between the ages of 17 and 35 living in NY State. The sampling procedure is devised to select a sample of 100 female college students with in the NY State. b. The population is defined to be all the people who shop at Green Acres Mall during the week before Christmas. The sampling procedure is devised to select every 25 th shopper who enters the Mall at only one of its ten entrances. c. The population is all the faculty members teaching at the College of Bill and Mary. The sampling procedure will select a sample of 25 faculty members using the following procedure: The name of each faculty member will be placed in a large drum. The drum is rotated several times before each of the 25 faculty names are selected. d. An advertising agency decides to conduct a marketing poll of people living in a New England community. The sampling procedure will draw a sample of people living within this community by selecting the names of the people from the community telephone directory. Section Uses of Statistics Statistics are used in many different fields such as economics, finance, psychology, sociology, education, and the physical sciences just to name a few. Extensive data collection and distribution activities are performed by the federal and other governmental and private agencies in areas such as education, employment, health, crime, prices, housing, medical care, manufacturing, agriculture, construction, transportation, etc. The development of the computer has led to a revolution in the area of data collection and analysis. Statistical analysis can now be applied to vast amounts of data accurately and quickly. Such diverse problems as weather forecasting, economic stabilization, and disease control are today being solved using statistical analysis. Section Misuses of Statistics The following techniques illustrate how information can be presented in a misleading fashion: 1. Misleading graphs - can be very misleading based on the scale. Example 1.15 on pg in Text An investment analyst could use a graph to show that the rate of return on retirement annuities are falling. 2. Non-representative samples (Biased) - purposely choosing a sample that favors your desired outcome. Example: Surveying people with a personal interest, such as their livelihood is dependent on a certain product Example: Surveying many people but only using the ones who say what you are looking for. 3

4 3. Inappropriate comparisons Example 1.21 on pg. 21 in Text During the gasoline shortage of the 70 s, people started buying foreign cars because they were more fuel efficient. A television commercial for an American automobile manufacturer showed two automobiles, the American-made auto and the foreign import, side-by-side. The commercial emphasized the Environmental Protection Agency s (EPA) fuel efficiency rating of the two autos which were shown in bold print as illustrated in Figure The omission of variation about an average Example 1.22 on pg. 21 in Text New mothers usually read many books about child development. However, these books can cause many unpleasant moments, especially if the reader misinterprets the author s statements concerning a child s development rate. For instance, a new mother may interpret A child begins to walk on average around 12 months, to mean that if her child does not walk by 12 months, her baby is abnormal or could be a late developer. Review the following examples in your textbook: Literary Digest on pg. 11, Example 1.13 on pg. 18, Example 1.17 on pg. 19, Example 1.19 on pg. 20, Example 1.20 on pg. 21 Class Worksheet - Chapter 1 Complete the following questions: 1. A survey of 1,000 undergraduates at a midwestern university of 40,000 undergraduates was taken to determine the percentage of undergraduates living at home. The survey concluded that 20% of the students live at home. a. What is the population? b. What is the sample? c. The percentage value 20% represents a 2. Parameters describe the characteristics of a 3. The use of sample information to estimate a population characteristic is the primary objective of statistics. Thus, the researcher must take care to insure that the sample is of the population. 4. Most psychology texts reports that the average IQ score for an adult male is between 90 and 110. This average is an example of a 4

5 Chapter 1 Homework assignment from the Textbook: pg # 1 12, 17, 19, 21, 23, 24, 25, 27 47, 49, 51, 53, 55, 57, 59, Before they are arranged or analyzed information or observations are called data. 2. The collection, presentation, analysis and interpretation of data is called 3. The study of statistics can be separated into two areas: statistics and statistics. 4. The branch of statistics that uses numerical and/or visual techniques to summarize data is called 5. The total collection of individuals or objects under consideration is called the 6. Inferential statistics is the process of using a sample to draw inferences or conclusions about a 7. A number that is used to describe a characteristic of a sample, such as a sample average, is called a 8. A study of all working women in San Francisco was conducted to determine their average annual salary. A sample of 250 working women was selected, and their salaries were recorded. a) The population is b) The sample is c) The population parameter being studied is 9. A research medical team, using data collected from a sample of 4000 sport-related injuries, reported that the average recovery time for a broken ankle is eight weeks. This average is an example of a: a) Parameter b) Statistic 10. The results of a survey indicate that 23% of the election district will support the proposition. This is an example of: a) Descriptive statistics b) Inferential statistics 11. Statistics describe the characteristics of a a) Population b) Sample 12. Which of the following is an example of a parameter? a) In a sample of 10,000 children under age fifteen, 2,466 play soccer. b) The average male SAT verbal score is 460. c) Sixty-seven out of 100 pollsters surveyed predict Mayor DePortoro will win the election. 5

6 Chapter 1 Homework assignment from the Textbook continued 17. The idea of selecting a sample to determine the characteristics of the population is the essence of statistics. 19. A survey that includes every item or individual of the population is called a 21. The objective of Inferential Statistics is to draw a conclusion about the entire using a 23. The size of a finite population is denoted by 24. A numerical characteristic of a population such as the population average is called a 25. A numerical characteristic of a sample such as the sample average is a 27. The symbol used to represent the size of a sample is a) N b) S c) X d) n 47. A survey was conducted to determine the opinion of people in a Miami suburb on a proposed law to legalize casino gambling. A sample of 400 people were questioned. It was determined that 58% favored legalizing casino gambling. a) The population is b) The sample is c) The percentage value, 58%, is a statistic because it describes a characteristic of a 49. The average age of those surveyed is years. This is an example of a) Descriptive statistics b) Inferential statistics 51. Inferential statistics helps researchers make generalizations about large populations by using data from a sample of the population. (T/F) 53. In applications of inferential statistics all the observations of the population should be obtained. (T/F) 55. If a sample is not representative of the population, inferences made from the sample information may not be correct. (T/F) 57. A random sample will always be a representative sample. (T/F) 59. A United States senator mailed a questionnaire to all the constituents living in her state. She randomly selected 200 of the questionnaires which were returned to her office. Would this sample represent a random sample of all the constituents living in her state? Explain your answer. 61. CCC, a television network, decides to poll its viewers on gun control. The network requests its viewers to call GUNSYES if they are against gun control. All viewers who favor gun control are asked to call GUNSSNO. Do you believe this sampling procedure represents an appropriate technique in obtaining a random sample of the all the viewers of CCC regarding their views on gun control? Explain. 6