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# Hyp A

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### Transcript

• 1. Basic Business Statistics (8 th Module) Chapter 9 Fundamentals of Hypothesis Testing: One-Sample Tests
• 2. Chapter Topics
• Hypothesis Testing Methodology
• Z Test for the Mean ( Known)
• p-Value Approach to Hypothesis Testing
• Connection to Confidence Interval Estimation
• One-Tail Tests
• t Test for the Mean ( Unknown)
• Z Test for the Proportion
• Potential Hypothesis-Testing Pitfalls and Ethical Issues
• 3. What is a Hypothesis?
• A Hypothesis is a Claim (Assumption) about the Population Parameter
• Examples of parameters are population mean or proportion
• The parameter must be identified before analysis
I claim the mean GPA of this class is 3.5! © 1984-1994 T/Maker Co.
• 4. Testing of hypothesis
• The process of accepting rejecting a statistical hypothesis based on sampling is called testing of hypothesis.
• Eg: The Hypothesis 5% of people in a city A-Are suffering from TB is a Statistical Hypothesis.
• Taking a random sample of the size n from the population of the city, calculating the proportion of the individuals suffering from TB and deciding whether we have to accept or reject the hypothesis is called Statistical Test .
• 5. The Null Hypothesis, H 0
• States the Assumption (Numerical) to be Tested
• E.g., The mean GPA is 3.5
• Null Hypothesis is Always about a Population Parameter ( ), Not about a Sample Statistic ( )
• Is the Hypothesis a Researcher Tries to Reject
• 6. The Null Hypothesis, H 0
• Begin with the Assumption that the Null Hypothesis is True
• Similar to the notion of innocent until proven guilty
• Refer to the Status Quo
• Always Contains the “=” Sign
• The Null Hypothesis May or May Not be Rejected
(continued)
• 7. The Alternative Hypothesis, H 1
• Is the Opposite of the Null Hypothesis
• E.g., The mean GPA is NOT 3.5 ( )
• Challenges the Status Quo
• Never Contains the “=” Sign
• The Alternative Hypothesis May or May Not Be Accepted (i.e., The Null Hypothesis May or May Not Be Rejected)
• Is Generally the Hypothesis that the Researcher Claims
• 8. Error in Making Decisions
• Type I Error
• Reject a true null hypothesis
• When the null hypothesis is rejected, we can say that “We have shown the null hypothesis to be false (with some ‘slight’ probability, i.e. , of making a wrong decision)
• Has serious consequences
• Probability of Type I Error is
• Called level of significance
• Set by researcher
• 9. Type 1 Error (  )
• The size of a test is the probability of rejecting null hypothesis when it is true.It is denoted by and this type of error is called Type 1 error
•   =P(reject H 0/ H 0 )
• Rejecting H0 , when H0 is True (Rejecting a True Hypothesis). Eg;
• 10. Type 2 Error(  )
• Accepting H0 when H0 is False(Accepting a wrong Hypothesis).
 = Accept(H0/H1)
• 11. Error in Making Decisions
• Type II Error
• Fail to reject a false null hypothesis
• Probability of Type II Error is
• The power of the test is
• Probability of Not Making Type I Error
• Called the Confidence Coefficient
(continued)
• 12. Power of a Test
• Consider the case when the Hypothesis H 0 is not True, then there is a possibility of H 1 is True.
• Power of a test is defined as the probability of rejecting the null hypothesis when it is actually false ie when H 1 is true.
• Power=P(reject H0/H1)
• =1 – P(Accept H 0 /H 1 )
• = I – PROBABILITY OF TYPE 11 ERROR
• = I - 
• 13. Thanks
• 14. Standard Error
• The standard deviation of a statistic is called standard error of statistic.
• Let X1,X2 etc be the means of possible samples of size n drawn from a population, the standard deviation of the sample ,means the standard error of these means. This is found to be  /  n, where  is the population standard deviation and n is the sample size.
• 15. Degrees of Freedom
• The number of degrees of freedom in a problem, distribution, etc., is the number of parameters which may be independently varied . It is the no of independent observations in a set’
• If we are choosing any 5 nos. , whose total is 100, we can exercise our independent choice for any 4 nos. Only the 5 th no. is fixed by virtue of the total being 100. In this example there is only 1 restriction in our freedom. Therefore the degrees of freedom is 4.
• 16. Significance Level
• The significance level of a statistical hypothesis test is a fixed probability of wrongly rejecting the null hypothesis H 0 , if it is in fact true.
• 17. Statistic
• A statistic (singular) is the result of applying a statistical algorithm to a set of data . In the calculation of the arithmetic mean , for example, the algorithm directs us to sum all the data values and divide by the number of data items. In this case, we call the mean a statistic.
• 18. Test Statistic
• A test statistic is a quantity calculated from our sample of data. Its value is used to decide whether or not the null hypothesis should be rejected in our hypothesis test.
• 19. Critical Value(s)
• The critical value(s) for a hypothesis test is a threshold to which the value of the test statistic in a sample is compared to determine whether or not the null hypothesis is rejected.
• 20. Critical Region
• The critical region CR , or rejection region RR , is a set of values of the test statistic for which the null hypothesis is rejected in a hypothesis test; that is, the sample space for the test statistic is partitioned into two regions; one region (the critical region) will lead us to reject the null hypothesis H 0 ', the other not. So, if the observed value of the test statistic is a member of the critical region, we conclude 'reject H 0 '; if it is not a member of the critical region then we conclude 'do not reject H 0 .
• 21. Thanks