Inferential Statistics:

Transcription

1 AP Statistics

2 Inferential Statistics: Statistical Inference the process of drawing conclusions about the nature of a population based on data from a sample. Study observing individuals and measuring variables of interest. Experiment deliberately imposing some treatment on individuals in order to observe their responses.

3 Census: An attempt to contact every individual in the entire population to collect information about that population. A population is an entire group of individuals that we want information about.

4 Sampling: Sample the part of the population we actually examine in order to gather information. Sampling allows us to study a portion to get information about an entirety. A sample must represent the population as much as possible so results/conclusions will generalize. Thus, sampling techniques and methods must be chosen and executed properly.

5 Example Population: All MHS students. Sample: Students who came to the football game against De Soto.

6 Sampling Design The method used for choosing the sample. Your method for choosing a sample must be defensible.

7 Bias in a sample: Bias - systematically favoring certain outcomes. When a sample is biased, it misses the mark because some parts of the population are favored over others. Not all the subjects have the same chance of being picked. Voluntary Response Sampling and Convenience Sampling (which follow) are both biased.

8 Voluntary Response Sample: People choose themselves by responding to a general appeal. Source of Bias: Persons with strong opinions are overrepresented.

9 Convenience Sample: People who are easiest to reach are chosen. These include mall shoppers/pollsters. Source of Bias: Convenience samples miss getting a good cross-section of subjects (undercoverage).

10 *Note: There is always error in sampling. Sampling errors cannot be avoided. Three categories of sampling errors: Random Sampling Error - chance variation. Sampling Method Error - error that occurs because of the choice of a sampling method. Non-sampling Error - error occurs in the responses by individuals in the sample.

11 Probability Sampling Any method of sampling that utilizes some form of random selection. This is the general framework for all defensible sampling. The idea (in almost every case) is to give each individual in the population the same chance (greater than zero) of being selected. The following methods are all types of probability sampling.

12 Exercise 5.1 FUNDING FOR DAY CARE A sociologist wants to know the opinions of employed adult women about government funding for day care. She obtains a list of the 520 members of a local business and professional women s club and mails a questionnaire to 100 of these women selected at random. Only 48 questionnaires are returned. What is the population in this study? What is the sample?

13 Ex. 5.2 WHAT IS THE POPULATION? For each of the following sampling situations, identify the population as exactly as possible. That is, say what kind of individuals the population consists of and say exactly which individuals fall in the population. If the information given is not complete, complete the description of the population in a reasonable way.

14 Ex 5.2 (a) Each week, the Gallup Poll questions a sample of about 1500 adult U.S. residents to determine national opinion on a wide variety of issues.

15 Ex 5.2 (b) The 2000 census tried to gather basic information from every household in the United States. But a long form requesting much additional information was sent to a sample of about 17% of households.

16 Ex 5.2 (c) A machinery manufacturer purchases voltage regulators from a supplier. There are reports that variation in the output voltage of the regulators is affecting the performance of the finished products. To assess the quality of the supplier s production, the manufacturer sends a sample of 5 regulators from the last shipment to a laboratory for study.

17 Exercise 5.7 CALL THE SHOTS A newspaper advertisement for USA Today: The Television Show once said: Should handgun control be tougher? You call the shots in a special call-in poll tonight. If yes, call If no, call Charge is 50 cents for the first minute. Explain why this opinion poll is almost certainly biased.

18 Exercise 5.8 EXPLAIN IT TO THE CONGRESSWOMAN You are on the staff of a member of Congress who is considering a bill that would provide government-sponsored insurance for nursing home care. You report that 1128 letters have been received on the issue, of which 871 oppose the legislation. I m surprised that most of my constituents oppose the bill. I thought it would be quite popular, says the congresswoman. Are you convinced that a majority of the voters oppose the bill? How would you explain the statistical issue to the congresswoman?

19 Simple Random Sampling (SRS) The sample is chosen in such a way that every set of n individuals has an equal chance of being selected. This may be accomplished using technology, or using a Random Number (Digit) Table.

20 Random Digit Table Table B in the back of the textbook. Uses long strings of digits from 0-9 where each entry is equally likely and the entries are independent of each other.

21 Independence Knowledge of one outcome gives no information about the next outcome.

22 Sampling Frame The list of individuals from which a sample is actually selected.

23 Steps for using a Random Digit Table: Assign a numerical label of equal length to each member of the group. Use table B to select labels at random. Since the table has no order, you may start at any row and proceed in any systematic fashion.

24 5.10 WHO SHOULD BE INTERVIEWED? A firm wants to understand the attitudes of its minority managers toward its system for assessing management performance. Below is a list of all the firm s managers who are members of minority groups. Use Table B at line 139 to choose 6 to be interviewed in detail about the performance appraisal system. (SEE Example 5.4 on pg.276)

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