Lecture PowerPoint Slides Basic Practice of Statistics 7 th Edition

me a picture of your NIH certification by Friday Have questions on the Chapter 12 Quiz? (optional, but due Fri.) Figure out a way to collect data for your project

Statistical estimation Population Sample Collect data from a representative Sample... Make an Inference about the Population. The process of statistical inference involves using information from a sample to draw conclusions about a wider population. Different random samples yield different statistics. We need to be able to describe the sampling distribution of possible statistic values in order to perform statistical inference.

Sampling distribution of the mean

The 3 distributions

Parameters and statistics

The Law of Large Numbers

Sampling distributions The population distribution of a variable is the distribution of values of the variable among all individuals in the population. The sampling distribution of a statistic is the distribution of values taken by the statistic in all possible samples of the same size from the same population. Be careful: The population distribution describes the individuals that make up the population. A sampling distribution describes how a statistic varies in many samples from the population.

Unnumbered art Page 347, The Basic Practice of Statistics, © 2015 W. H. Freeman, Jupiterimages/Getty Images Dimethyl Sulfide Threshhold

Figure 15.2, The Basic Practice of Statistics, © 2015 W. H. Freeman

Figure 15.3, The Basic Practice of Statistics, © 2015 W. H. Freeman

Figure 15.4a, The Basic Practice of Statistics, © 2015 W. H. Freeman Another example: Household earnings

Figure 15.4b, The Basic Practice of Statistics, © 2015 W. H. Freeman

Figure 15.4c, The Basic Practice of Statistics, © 2015 W. H. Freeman

Population distributions versus sampling distributions 15 There are actually three distinct distributions involved when we sample repeatedly and measure a variable of interest. 1)The population distribution gives the values of the variable for all the individuals in the population. 2)The distribution of sample data shows the values of the variable for all the individuals in the sample. 3)The sampling distribution shows the statistic values from all the possible samples of the same size from the population.

Exploring the 3 distributions Alternate applet (try this first)

Research Project Update Check Moodle description of project Start looking at articles (you’ll need 3) Get your data into a Google Sheet (or Excel)

me a picture of your NIH certification by Friday Have questions on the Chapter 12 Quiz? (optional, but due Fri.) Chapter 15 Quiz due by Friday Project: Raw vs. aggregate data

The 3 distributions

Distribution of Population Distribution of Sample Means (Sampling Distribution of the Mean) Distribution of Sample ?

Let’s get random partners and try out some problems

Blood pressure

The central limit theorem

Figure 15.5, The Basic Practice of Statistics, © 2015 W. H. Freeman n = 2 n = 10 n = 25 population How large of a sample size (n) do we need for the Central Limit Theorem to kick in and let us assume a Normal distribution?

Legal action about advertising

Do the 14 oz. Halloween Reese’s pieces bags really have 14 oz. of candy or is it false advertising? 14 oz.

Questions to ponder… Would our answer have been different to the Reese’s Pieces question if the original distribution was NOT Normal? Would it matter if we bought all 100 bags from Costco? Would our answer have been different to the Reese’s Pieces question if we had only used a sample size of 5 bags instead of 100?

Central limit theorem: example 30 Based on service records from the past year, the time (in hours) that a technician requires to complete preventative maintenance on an air conditioner follows the distribution that is strongly right-skewed, and whose most likely outcomes are close to 0. The mean time is µ = 1 hour and the standard deviation is σ = 1. Your company will service an SRS of 70 air conditioners. You have budgeted 1.1 hours per unit. Will this be enough? The central limit theorem states that the sampling distribution of the mean time spent working on the 70 units has: The sampling distribution of the mean time spent working is approximately N(1, 0.12) since n = 70 ≥ 30. If you budget 1.1 hours per unit, there is a 20% chance the technicians will not complete the work within the budgeted time.

Airline Loads Airlines are told to assume that passengers weigh, on average, 190 lbs. Let’s assume that weight is Normally distributed (it almost is), and that the standard deviation of people’s weights is 35 lbs. What is the chance that a random set of 22 passengers will have a total weight greater than 4500 lbs? P(wt > 4500) = P(x bar > ) = P(Z > 1.95) =.0256

Sampling distributions and statistical significance We have looked carefully at the sampling distribution of a sample mean. However, any statistic we can calculate from a sample will have a sampling distribution. The sampling distribution allows us to determine the probability of observing any particular value of the sample statistic in another such sample from the population.

Why should we do this? NGOs in Uganda: How can relief money be used most effectively?

Increase education in Kenya: Free textbooks?

Poverty Action Lab

Evidence Action

MCAT Scores To estimate the mean score of MCAT students on your campus, you will select a Simple Random Sample of students. You know already that scores are approximately Normal with a standard deviation of 6.5. How big should your sample be to reduce the standard deviation of the sample mean to 1?

The 3 distributions

Studies on Water, Sanitation, and Hygiene (WASH) Sustainability

#1 Halloween Candy? Overall? In most states? In Virginia?