The Population vs. The Sample We will likely never know these (population parameters - these are things that we want to know about in the population) The population Number = N Mean = m Standard deviation = s Cannot afford to measure parameters of the whole population

3 General Kinds of Sampling Haphazard sampling Based on convenience and/or self-selection Street-corner interview, mall intercept interview Television call-in surveys, questionnaires published in newspapers, magazines, or online Literary Digest poll (2 million) versus George Gallup poll (2,000) before the 1936 election

3 General Kinds of Sampling Quota sampling Categories and proportions in the population More representative than quota sampling Interviewers have too much discretion Probability sampling A sample of a population in which each person has a known chance of being selected Basically an equal chance at the start

Size of a Probability Sample Depends on: Accuracy (margin of error) typically +/-3% Confidence level: probability that the results are outside the specified level of accuracy Variability: researchers usually assume maximum variability for a binomial variable Random sampling Multistage cluster sampling

The Population vs. The Sample We will likely never know these (population parameters - these are things that we want to know about in the population) The population Number = N Mean = m Standard deviation = s Cannot afford to measure parameters of the whole population So we draw a random sample.

The Population vs. The Sample The sample Sample size = n Sample mean = x Sample standard deviation = s Cannot afford to measure parameters of the whole population So we draw a random sample.

The Population vs. The Sample Does m = x? Probably not. We need to be confident that x does a good job of representing m. The population Number = N Mean = m Standard deviation = s The sample Sample size = n Sample mean = x Sample standard deviation = s

Connecting the Population Mean to the Sample Mean How closely does our sample mean resemble the population mean (a “population parameter” in which we are ultimately interested)? Population parameter = sample statistic + random sampling error (or “standard error”) Random sampling error = (variation component) . or “standard error” (sample size component) Use a square-root function of sample size The sample Sample size = n Sample mean = x Sample standard deviation = s s = measure of variation Standard error (OR random sampling error) = s . Ö (n-1) Population mean = x + s . Ö (n-1) The population mean likely falls within some range around the sample mean—plus or minus a standard error or so.

To Compute Standard Deviation Population standard deviation Sample standard deviation

Why Use Squared Deviations? Why not just use differences? Student A’s exam scores/(Stock A’s prices): 94, 86, 94, 86 Why not just use absolute values? Student B’s exam scores/(Stock B’s prices): 97, 84, 91, 88 Which one is more spread out /unstable /risky /volatile?

is the formula for: Population standard deviation Sample standard deviation Standard error Random sampling error Population mean