Chapter 9 Probability

2 More Statistical Notation  Chance is expressed as a percentage  Probability is expressed as a decimal  The symbol for probability is p

3 Probability The probability of an event is equal to the event’s relative frequency in the population of possible events that can occur.

Obtaining Probability from the Standard Normal Curve

5 Probability of Individual Scores The proportion of the total area under the normal curve for scores in any part of the distribution equals the probability of those scores.

6 Obtaining Probability To compute probability, use the same techniques you learned for finding the area under the normal curve using z scores and the z-tables.

7 Z-distribution Showing the Area for Scores Below the Mean, and Between the Mean and Z = +1

Making Decisions Based on Probability

9 Representativeness  Any sample may poorly represent one population, or it may accurately represent a different population  The essence of inferential statistics is to decide whether a sample of scores is likely or unlikely to occur in a particular population of scores

10 Region of Rejection  At some point, a sample mean is so far above or below the population mean that it is unbelievable that chance produced such an unrepresentative sample  The areas beyond these points is called the region of rejection  The region of rejection is the part of a sampling distribution containing values that are so unlikely that we “reject” that they represent the underlying raw score population

11 Means in the Region of Rejection Are So Unrepresentative of This Population That It’s a Better Bet They Represent Some Other Population.

12 Criterion The criterion is the probability that defines samples as too unlikely for us to accept as representing a particular population.

13 Rejection Rule  When a sample’s z-score lies beyond the critical value, reject that the sample represents the underlying raw score population reflected by the sampling distribution  When the z-score does not lie beyond the critical value, retain the idea that the sample may represent the underlying raw score population

Sampling Error  When the sample statistic is not identical to the population parameter  Amount of error between a sample statistic & its corresponding population parameter - Different samples from same population

Distribution of Sample Means  Collection of sample means for all the possible random samples of a particular size (n) that can be obtain from a population  To predict characteristics of distribution Sample means should pile up around pop mean Pile should form normal distribution Larger sample size  closer sample means to pop mean

Central Limit Theorem  Distribution of sample means approach a normal dist. as N approaches infinitiy  Dist. Of sample means tends to be normal if: Pop from which samples selected is normal Number of scores is relatively large, n=30

Standard Error of the Mean  Standard deviation of the distribution of sample means  SE measures the standard amount of difference between sample mean and the pop mean  estimate!!