Section 9

# Section 9 - Statistics An Introduction Fifth Edition...

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1 Statistics: An Introduction Fifth Edition 374 Section 9: Hypothesis Testing A. The Problem (3 scenarios) Poll. Possibilities: In past, advisers spent 4 hours/week advising. Is program to increase time advising effective? Possibilities: Which method for teaching reading is better? Possibilities: 1 .5, 1 .5, 1 .5 4, 4, 4 1 2 , 1 2 , 1 2 375 Section 9: Hypothesis Testing B. Logic of Hypothesis Testing 1. List all possibilities. 2. Hypothesize one possibility is true. 3. Seek evidence to show that it is unlikely that possibility is true. 4. If such evidence is found, reject that possibility. 5. Repeat steps 2, 3, and 4 until only one possibility remains.

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2 376 Section 9: Hypothesis Testing Example: Poll 1. Possibilities 2. Hypothesize 3. Conduct poll using a random sample of n =100 and find p =.7. 4. Decide whether evidence is sufficient to reject hypothesis in 2. 1 .5, 1 .5, 1 .5 1 .5 377 Section 9: Hypothesis Testing Comments: In hypothesis testing, null hypothesis is typically stated. Is the “equality hypothesis.” If evidence is found that indicates the null hypothesis unlikely, it is “rejected” and an alternative hypothesis is “accepted.” If insufficient evidence is found to indicate it is unlikely, the null hypothesis is “retained” as possibly true. Statistical theory is used in this process – based on uncertainty. Cannot prove that one of the hypotheses is true. 378 Section 9: Hypothesis Testing C. Formal Hypothesis Testing Step 1. State the statistical hypothesis to be assumed true. Is null hypothesis ( ). State the alternative hypotheses. Step 2. State level of significance, the acceptable risk of rejecting the null hypothesis when it is true. Step 3. Specify the critical region to use. Is values of the statistic for which the null hypothesis should be rejected. H 0
379 Section 9: Hypothesis Testing Step 4. Carry out the study and compute the test statistic. Step 5. Compare the statistic in Step 4 with the critical region in Step 3. Either retain or reject the null hypothesis. If null hypothesis is rejected, accept an alternative hypothesis. 380 Section 9: Hypothesis Testing Hypothesis Testing Example In past, advisers spent 4 hours/week advising. Program is introduced to increase advising. Is program effective? 1. State null and alternative hypotheses. 2. State level of significance. H 0 : 4 H 1 : 4 H 2 : 4 .05 381 Section 9: Hypothesis Testing 3. Find Critical Value Sampling distribution for mean is normally distributed. Called critical region R.

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## This note was uploaded on 10/11/2011 for the course STAT 102 taught by Professor Jimmaxey during the Spring '11 term at Iowa State.

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Section 9 - Statistics An Introduction Fifth Edition...

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