Sampling Variability Section 8.1

Let’s explore Find a point estimate of the area of the rectangles on the page. How many should we sample? Use Math – PRB – RandInt(1,100, n)

Questions Do all of your trials contain the true mean of 7.4? What’s the shape of the graph? If mean is 7.4 and standard deviation is 5.126 , what is the mean & standard deviation of the sampling distribution?

Sampling Distribution Represents the long run behavior of the mean when sample after sample is selected. It is used to find out more about a parameter of a population.

Parameter Quantity computed from values in a population Usually not known

Statistic Quantity computed from values in a sample. Computed directly from sample data

Identify the population, parameter, sample and statistic. 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.”

Identify the population, parameter, sample and 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 of iced tea.

Identify the population, parameter, sample and statistic. 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.

Sampling Variability The observed value of a statistic will depend on the sample selected. In other words – it will vary from sample to sample.

Sampling Distribution Distribution of the values of a statistic Notice what the relationship is between the mean of the population & the sample.

Abby -24 Bill – 25 Cindy- 26 Dave – 27 Ed – 28 Find the sampling distribution if we look at samples of size 2. (sample with replacement – do all combinations!)

{2, 4, 6, 8} – Size 2 samples - mean

{2, 4, 6, 12} – Size 2 samples - range

Unbiased Estimator If the mean of the sampling distribution is equal to the true value of the parameter being estimated.

Sampling Heights Write name and height in inches on paper. Each person will take a sample of 4. Find the sample mean – put on dotplot Find the sample range – put on dotplot

Variability of a Statistic The spread of the sampling distribution does not depend on the size of the population, as long as the population is at least 10 times larger than the sample size.

Homework Page 428 (1-19)odd, (21-24) For the population {10, 12, 14, 16}, find the following for a sample size of 2: A. Sampling distribution of means B. Sampling distribution of range