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Chapter 6 Hypotheses texts. Central Limit Theorem Hypotheses and statistics are dependent upon this theorem.

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Presentation on theme: "Chapter 6 Hypotheses texts. Central Limit Theorem Hypotheses and statistics are dependent upon this theorem."— Presentation transcript:

1 Chapter 6 Hypotheses texts

2 Central Limit Theorem Hypotheses and statistics are dependent upon this theorem

3 Central Limit Theorem To understand the Central Limit Theorem we must understand the difference between three types of distributions…..

4 A distribution is a type of graph showing the frequency of outcomes:

5 Of particular interest is the “normal distribution”

6 Different populations will create differing frequency distributions, even for the same variable…

7 There are three types of distributions: 1. Population distributions

8 There are three types of distributions: 1. Population distributions

9 There are three types of distributions: 1. Population distributions

10 There are three types of distributions: 1. Population distributions 2. Sample distributions

11 There are three types of distributions: 1. Population distributions 2. Sample distributions

12 There are three types of distributions: 1. Population distributions 2. Sample distributions 3. Sampl ing distributions

13 There are three types of distributions: 1. Population distributions The frequency distributions of a population.

14 There are three types of distributions: 2. Sample distributions The frequency distributions of samples. The sample distribution should look like the population distribution….. Why?

15 There are three types of distributions: 2. Sample distributions The frequency distributions of samples.

16 There are three types of distributions 3. Sampl ing distributions The frequency distributions of statistics.

17 There are three types of distributions: 2. Sample distributions The frequency distributions of samples. The sampling distribution should NOT look like the population distribution….. Why?

18

19 Suppose we had population distributions that looked like these:

20 Say the mean was equal to 40, if we took a random sample from this population of a certain size n… over and over again and calculated the mean each time……

21 We could make a distribution of nothing but those means. This would be a sampling distribution of means.

22 Central Limit Theorem If samples are large, then the sampling distribution created by those samples will have a mean equal to the population mean and a standard deviation equal to the standard error.

23 Type I and Type TT errors –Type I : reject the correct original Hypothesis , called Producer's Risk –Type II : accept the wrong original Hypothesis , called Consumer’s Risk Population condition conclu sion H o true H a true AcceptH 0 correct type TT error conclusion RejectH 0 Type I error correct conclusion

24 We denote the probabilities of making the two errors as follows: α——the probability of making a Type I error β——the probability of making a Type TT error In practice , the person conducting the hypothesis test specifies the maximum allowable probability of making a Type I error , called the level of significance for the test 。 Common choices for the level of significance are α=0.05 orα= 0.01 。 Type I and Type TT errors

25 Sampling Error = Standard Error

26 The sampling distribution will be a normal curve with: and

27 This makes inferential statistics possible because all the characteristics of a normal curve are known.

28

29 Errors:

30 Type I Error: saying something is happening when nothing is: p = alpha Type II Error: saying nothing is happening when something is: p = beta

31

32 Steps of Hypothesis Testing 1.Determine the null and alternative hypotheses. 2.Specify the level of significance . 3.Collect the sample data and calculate the test statistic. Using the p -Value 4.Use the value of the test statistic to compute the p - value. 5.Reject H 0 if p -value < .

33 Steps of Hypothesis Testing Using the Critical Value 4.Use  to determine the critical value for the test statistic and the rejection rule. 5.Use the value of the test statistic and the rejection rule to determine whether to reject H 0.

34 Thanks for Your Attention


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