Statistics The big picture...

Populations We want to learn about a population. A population is any large collection of objects or individuals, such as people, students, or trees about which information is desired. e.g. the heights of all Americans are: 74”, 58”, 72”, 65”, 68”, 71”, 71”, 69”, 63”, 63”, 66”, … e.g. the opinions of all college students about marijuana use is: Y, N, N, Y, Y, Y, N, Y,...

Parameters A population of measurements is too large to collect and too large to say anything meaningful about the population. A parameter is any summary number, like an average or proportion, that describes the entire population.

Parameters Examples include: –population mean  –population standard deviation  –population proportion p ….% of the time, we don’t (...or can’t) know the real value of a population parameter. It is unknown! Best we can do is estimate the parameter!

Samples A sample is a representative group drawn from the population. e.g. the heights of 10 Americans are: 74”, 58”, 72”, 65”, 68”, 71”, 71”, 69”, 63”, 66” e.g. the opinions of 20 college students about marijuana use is: Y, N, N, Y, Y, Y, N, Y, Y, Y, N, N, N, N, Y, N, N, Y, N, N

Statistics Because samples are manageable in size, we can determine the value of statistics. A statistic is any summary number, like an average or proportion, that describes the sample.

Statistics Examples include: –sample mean  –sample standard deviation s –the sample proportion (“p-hat”) We use the known statistic to estimate the unknown parameter.

Which parameter? Which statistic? The type of data collected determines: –the appropriate parameter, –the appropriate statistic, –the appropriate confidence interval, –and the appropriate hypothesis test. Proportions summarize categorical data. Means summarize numerical data.

Two ways to learn about a population parameter Confidence intervals estimate parameters. –We can be 95% confident that the proportion of Penn State students who have a tattoo is between 5.1% and 15.3%. Hypothesis tests test the value of parameters. –There is enough statistical evidence to conclude that the mean GPA of all Penn State science majors is greater than 3.0.

Is our class representative of PSU pop’n with respect to gender? Note that 55% of Penn State students are female. Conduct hypothesis test: –Specify hypotheses. –Collect sample data. –Define and determine P-value. –Make decision and draw conclusion. –Acknowledge possible errors.

Does data suggest that two cars A and B handle differently? The two cars have different lengths, wheel bases, and turning radii. Experiment conducted on 14 subjects. Measurements are time in seconds required for subjects to parallel park each car. Hypothesis test conducted. Results reported in paper “ Relative Controllability of Dissimilar Cars,” in journal Human Factors, 1962.