7.1 Introduction to Sampling Distributions GET A CALCULATOR!!!!

Inferential Statistics vs. Descriptive Statistics Inferential: RANDOMIZATION makes it possible to use probability to make inferences (the whole point of statistics – to make decisions) Descriptive: Describing a set of data. (What we’ve done so far)

Inferential Statistics vs. Descriptive Statistics Population Parameter Sample Statistic *values vary from sample to sample *used to estimate an unknown parameter *KNOWN – calculated from data *Fixed values, but often unknown µ σ p 𝑥 s 𝑝

Sampling Variability The value of a statistic varies in repeated random sampling.

Example, p. 425 Identify the population, the parameter, the sample, and the statistic in each of the following settings: (a) The Gallup Poll asked a random sample of 515 U.S. adults whether or not they believe in ghosts. Of the respondents, 160 said “Yes”. Population: U.S. adults Parameter: p Sample: 515 U.S. adults Statistic: 𝑝 = 160 515 =0.31

Example, p. 425 Identify the population, the parameter, the sample, and the statistic in each of the following settings: (b) During the winter months, the temperatures outside the Starnes’s cabin in Colorado can stay well below freezing for weeks at a time. To prevent the pipes from freezing, Mrs. Starnes sets the thermostat at 50°F. She wants to know how low the temperature actually gets in the cabin. A digital thermometer records the indoor temperature at 20 randomly chosen times during a given day. The minimum reading is 38°F. Population: All times during the day Parameter: µ Sample: 20 temperatures at randomly selected times Statistic: sample minimum = 38°F

Check Your Understanding, p. 425 Label the bold faced values as either a parameter or a statistic. On Tuesday, the bottles of Arizona Iced Tea filled in a plant were supposed to contain an average of 20 ounces of iced tea. Quality control inspectors sampled 50 bottles at random from the day’s production. These bottles contained an average of 19.6 ounces. Parameter: µ = 20 ounces Statistic: 𝑥 = 19.6 ounces   On a New York-to-Denver flight, 8% of the 125 passengers were selected for random security screening before boarding. According to the Transportation Security Administration, 10% of passengers at this airport are chosen for random screening. Parameter: p = 0.10 Statistic: 𝑝 = 0.08

What happens if we take many samples? Take a large number of samples from the same population Calculate sample mean or sample proportion for each sample Make a graph of the values 𝑥 or 𝑝 Examine the distribution displayed (SOCS) Could be expensive to take a large number of samples; we can use simulation.