Target for Today Know what can go wrong with a survey and simulation Know difference between a statistic and a parameter Write down the five steps for setting up a simulation Can make a sampling distribution Can determine confidence interval

Notes: Survey What can go wrong with a Survey? Volunteers: bias since only selected group voluntarily responds Convenience: who is easy to talk to does not always represent the whole population (people in prison, homeless) Sample Frame: frame may not include all important groups (if choose people from phone book lots not listed) Undercoverage: some groups not equally represented Non respondents: people who do not respond may represent an important group

Notes: Simulation What can go wrong with a Simulation? The simulation only tells you what might happen not what does happen You do not select the right numbers to reflect the outcome You do not run enough trials

What is the difference between a parameter and a statistic?

p.270 Statistic – is a numerical value computed from a sample. Parameter – is a numerical value associated with a population. Essentially, we would like to know the parameter. But in most cases it is hard to know the parameter since the population is too large. So we have to estimate the parameter by some proper statistics computed from the sample.

A closer look at some statistics

Sampling Distribution 1. Choose sample size n Run trials and find 𝑝 for each trail 3. Summarize results: a) Histogram for all 𝑝 b) Mean = 𝑝 # 𝑜𝑓 𝑡𝑟𝑖𝑎𝑙𝑠 c) Stdev =

The survey asks 200 random under-age students. A survey is undertaken to determine the proportion of PSU students who engage in under-age drinking. The survey asks 200 random under-age students. Suppose the true population proportion is 60% or p=.6

The proportion of under-age students who drink

A point estimate. Find by averaging all trials. Sample proportion (a statistic) A point estimate. Find by averaging all trials. 𝑝 = population proportion + random variation Standard deviation (use p if can otherwise 𝑝 ) or Problem with point estimate is it gives no information of how close the value is to the unknown population parameter

What are the steps for finding the Sampling Distribution for the PSU study?

Step #1: determine the sample size n Will 200 students be enough if the true proportion of students who drink is .6? #1: choose n Sample Size condition Need condition met to use the normal curve np > 10 and n(1-p)> 10 Where n = number in each trial P = population proportion

Step #2: Repeated Trials If we do this survey over and over and make a histogram of , what would the histogram look like? Sample (n=200) Sample Proportion 1 2 3 4 5 … 150,000 Imagine repeating this survey many times, and each time we record the sample proportion of those who have engaged in under-age drinking.

Summarize results with histogram 53% 67% 60%

How confident are you about But is p-hat enough information??? How confident are you about this statistic?

P-hat: point estimate A single number. No info on how accuracy of your statistic interval estimate Gives info on how close the statistic is to the real thing We are 68% confident that between 67% and 53% of PSU student drink underage Problem with point estimate is it gives no information of how close the value is to the unknown population parameter 53% 67% Upper Confidence Limit Lower Confidence Limit Point Estimate

Step #3: build confidence interval (CI) 99%: z = 2.58 95%: z = 1.96 90%: z = 1.64 The probability that the true population falls between two sets of values: lower confident limit: upper confident limit: Margin of Error Point Estimate Lower Confidence Limit Upper