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(1) In your own words explain the difference between "descriptive statistics" and "inferential statistics." Do not just give definitions.
(2) In your own words, define the four different sampling techniques.
(3)Develop your own hypothesis about a situation of interest, for example: "Middle income families containing four members spend 10% of their gross income on clothing per year."
(a) Select one of the four sampling techniques and give a detailed design of how you would gather sampling data to answer your hypothesis.
(b) Select a second sampling technique for the same hypothesis and give a second detailed design of how you would gather sampling data.
|(1) Descriptive statistics are used to organize or summarize a data set. That is, descriptive statistics “describe” the data that has been collected. For example, |
|the arithmetic average (mean) may be used as a “descriptive measure” for the number of workers who kept away from work during the 5-day strike. The census of any |
|country is another example of descriptive statistics. In this case, the information that is gathered concerning gender, race, income, etc. is compiled to describe |
|the population of the country at the point of time. A baseball player's batting average is another example of a descriptive statistic. It describes the player's |
|past ability to hit a baseball at any point in time. As we observe , all three examples given above organize, summarize, and describe a set of data. |
|Inferential statistics are applied to draw inferences about a population using data gathered from a sample. For example, we could take the information gathered |
|from a sample of employees on job satisfaction and draw inference about the general level of job satisfaction among the employees of the entire organization. |
|Opinion polls and television ratings systems represent other applications of inferential statistics. For example, a limited number of people are polled during an |
|election (exit poll) and then this information is used to describe the voting trends as a whole. |
| |
|(2) (a) Simple Random Sampling is a technique in which each unit of the population has the same chance of being included in the sample. The bias of the |
|investigator is kept out and inclusion of one unit into the sample does not influence the inclusion or non-inclusion of the others. Therefore the sample is a true |
|representative of the population. |
|(b) Cluster sampling is a technique where sampling happens in two or more stages. First-stage samples are drawn (say by simple random sampling) from the |
|population, and from these samples, second-stage samples are drawn, either using simple random sampling or by any other method. Stages may be added as required. |
|(c) Systematic random sampling is a technique in which the first unit is randomly selected from the population and additional units are taken at equal intervals |
|from the first unit to form the sample. The sampling interval k is given by k = N/n, where N = size of the population and n = size of the sample. |
|(d) Stratified random sampling is a technique in which the population is first divided into different strata with some distinguishing characteristics. Each stratum|
|is assigned a particular proportion and a random sample of a particular size is drawn from it, so that the final sample is made up of a particular proportion of |
|individuals from each stratum. |
| |
|(3) Hypothesis: The average coffee consumption in the population is 5 cups per week |
|(a) Simple random sampling- Select about 100 coffee drinkers randomly and ask them how much coffee they consume per week, on an average. Record the data. Tabulate,|
|construct descriptive statistics such as mean and standard deviation. Now we have enough information to do a hypothesis test. |
|(b) Cluster sampling- Select about 120 coffee drinkers, 40 from each of the three regions which are known to have light, moderate and heavy coffee drinking habits.|
|Ask them how much coffee they consume per week, on an average. Pool the information. Tabulate, construct descriptive statistics such as mean and standard |
|deviation. Now we have enough information to do a hypothesis test. |
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