1. © 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Chapter Nine Using Probability To Make Decisions about Data

2. © 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Chapter 9 - 2 New Statistical Notation Odds are expressed as fractions or ratios Chance is expressed as a percentage Probability is expressed as a decimal The symbol for probability is p

3. © 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Chapter 9 - 3 Probability The probability of an event is equal to the event’s relative frequency in the population.

4. © 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Random Sampling Random sampling is selecting a sample in such a way that all elements or individuals in the population have an equal chance of being selected. Chapter 9 - 4

5. © 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Chapter 9 - 5 Computing Probability

6. © 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Chapter 9 - 6 Probability Distributions A probability distribution indicates the probability of all events in a population –An empirical probability distribution is created by measuring the relative frequency of every event in the population –A theoretical probability distribution is a theoretical model of the relative frequencies of events in a population

7. © 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Chapter 9 - 7 Independent and Dependent Events Two events are independent events when the probability of one is not influenced by the occurrence of the other Two events are dependent events when the probability of one is influenced by the occurrence of the other

8. © 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Chapter 9 - 8 Sampling With and Without Replacement When sampling with replacement, any previously selected individuals or events are replaced back into the population before drawing additional ones When sampling without replacement, previously selected individuals or events are not replaced in the population before selecting again

9. © 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Chapter 9 - 9 Obtaining Probability from the Standard Normal Curve

10. © 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Chapter 9 - 10 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.

11. © 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Chapter 9 - 11 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.

12. © 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Probability of Sample Means Using the sampling distribution of means, we can determine the probability of sample means. Use Chapter 9 - 12

13. © 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Chapter 9 - 13 Random Sampling and Sampling Error

14. © 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Chapter 9 - 14 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

15. © 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Chapter 9 - 15 Representative Sample In a representative sample, the characteristics of the individuals and scores in the sample accurately reflect the characteristics of individuals and scores found in the population.

16. © 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Chapter 9 - 16 Sampling Error Sampling error occurs when, by chance, the scores that are selected produce a sample statistic that is different from the population parameter it represents.

17. © 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Chapter 9 - 17 Deciding Whether a Sample Represents a Population

18. © 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Chapter 9 - 18 Region of Rejection The region of rejection contains means that are so unlikely to be representing the underlying population we reject they represent that population

19. © 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Chapter 9 - 19 Means in the Region of Rejection Are So Unrepresentative of This Population It’s a Better Bet They Represent Some Other Population.

20. © 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Chapter 9 - 20 Criterion The criterion probability is the probability that defines samples as too unlikely for us to accept as representing a particular population.

21. © 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Identifying the Critical Value The critical value of z defines the minimum value of z a sample must have in order to be in the region of rejection A sample mean lies in the region of regression only if its z-score is beyond the critical value Chapter 9 - 21

22. © 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Chapter 9 - 22 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

23. © 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. One-Tailed Tests When testing for sample means that are less than a given value, the entire region of rejection is in the left-hand tail Chapter 9 - 23

24. © 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Chapter 9 - 24 One-Tailed Tests When testing for sample means that are greater than a stated value, the entire region of rejection is in the right-hand tail

25. © 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Key Terms criterion probability critical value dependent event independent event inferential statistics p probability probability distribution Chapter 9 - 25 random sampling region of rejection representative sample sampling error sampling with replacement sampling without replacement