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Hyp A

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  • 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

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