Chapter 7.6 M2

Sample Data & Populations

EQ: How can we collect data from

populations?

The Sample Plan is the process followed to select units from the population to be used

in the sample

Basic Concepts in Samples and Sampling

• Population: the entire group under study as defined by research objectives. Sometimes called the “universe.”

Researchers define populations in specific terms such as heads of households, individual person types, families, types of retail outlets, etc. Population geographic location and time of study are also considered.

Basic Concepts in Samples and Sampling

• Sample: a subset of the population that should represent the entire group

• Sample unit: the basic level of investigation…consumers, store managers, shelf-facings, teens, etc. The research objective should define the sample unit

• Census: an accounting of the complete population

Basic Concepts in Samples and Sampling…cont.

• Statistic: a numerical description of a sample characteristic

• parameter: a numerical description of a population characteristic. The mean of a population is an example of a population parameter.

• Population mean: The true mean of the entire population

Reasons for Taking a Sample

• Practical considerations such as cost and population size

• Inability of researcher to analyze large quantities of data potentially generated by a census

• Samples can produce sound results if proper rules are followed for the draw

Probability Sampling MethodsSimple Random Sampling

• Simple random sampling: the probability of being selected is “known and equal” for all members of the population• Blind Draw Method (e.g. names “placed in a hat”

and then drawn randomly)• Random Numbers Method (all items in the

sampling frame given numbers, numbers then drawn using table or computer program)

• Advantages: • Known and equal chance of selection• Easy method when there is an electronic database

Ex 1: Collect data by random sampling

• A country club has 345 social members and 876 golf members. The president of the country club wants to form a random sample of 20 social members and a separate random sample of 50 golf members to answer some survey questions. Each social member has a membership number from 1-345 and each golf member has a membership number from 1001 to 1876. Use a graphing calculator to select the members who will participate in each random sample.

The SolutionKeystrokes: math, prb, 5(randInt)

• Use the random integer feature of a graphing calculator to generate 20 random integers between 1 and 345.

• Use the arrows to scroll over and see the rest of the random values.

• Document the values – this list makes up your random sample of social members.

• Now use the random integer feature to generate 50 random integers between 1001 and 1876.

• Use the arrows to scroll over and see the rest of the random values.

• Document the values – this list makes up your random sample of golf members.

Ex2: Compare statistics and parameters

• A school’s math club wants to know how many hours students spend on math homework each week. Savannah and Miguel, two students in the math club, collect separate random samples. Their results are displayed on page 274 of the M2 textbook.

• The population mean is 11.9 and the population standard deviation is about 6.7. Compare the means and the standard deviations of the random samples to the population parameters.

Let’s compare results

• Savannah• X-bar: 9.8• Std. deviation: 3.6

• Miquel• X-bar: 12.7• Std. deviation: about 4.2

•The mean of Savannah’s sample is less than the population mean.

•The mean of Miguel’s sample is greater than the population mean.

•The standard deviations of both samples are less than the population standard deviation.

•This indicates that the samples are less varied than the entire population.

Homework

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