Your SlideShare is downloading. ×
Hyp A
Upcoming SlideShare
Loading in...5

Thanks for flagging this SlideShare!

Oops! An error has occurred.

Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Text the download link to your phone
Standard text messaging rates apply

Hyp A


Published on

Published in: Business
No Downloads
Total Views
On Slideshare
From Embeds
Number of Embeds
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

No notes for slide


  • 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
  • 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
  • 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 - 
  • 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