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Hyp A
 

Hyp A

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    Hyp A Hyp A Presentation Transcript

    • Basic Business Statistics (8 th Module) Chapter 9 Fundamentals of Hypothesis Testing: One-Sample Tests
    • 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
    • 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.
    • 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 .
    • 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
    • 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)
    • 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
    • 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
    • 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;
    • Type 2 Error(  )
      • Accepting H0 when H0 is False(Accepting a wrong Hypothesis).
       = Accept(H0/H1)
    • 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)
    • 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 - 
    • Thanks
    • 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.
    • 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.
    • 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.
    • 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.
    • 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.
    • 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.
    • 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 .
    • Thanks