1. HYPOTHESIS TESTING ALLPPT.com _ Free PowerPoint Templates, Diagrams and Charts By: Sathish Rajamani Associate Professor VNC - Panipat

2. PREVIEW 1.Hypothesis Definition 2.Types of Hypothesis 3.Statistics Types 4.Inferential Statistics 5.Basic Concepts in Hypothesis Testing 6.Procedure for Hypothesis Testing

3. HYPOTHESIS A hypothesis is a tentative statement about the relationship between two or more variables. Example: Drinking sugary drinks daily leads to obesity.

4. TYPES OF HYPOTHESIS I.Simple Vs. Complex II.Associative Vs. Causal III.Directional Vs. Non – Directional IV.Null Vs. Alternative (Statistical Vs. Research)

5. Types of Statistics Descriptive Statistics Used to describe the basic features of the data in a study. 1. Collect Data: e.g. Survey 2. Present Data: e.g. Tables & Graphs 3. Measures of Central Tendency 4. Measures of Dispersion Inferential Statistics Drawing conclusions and / or making decisions concerning a population based on a sample results. 1.Estimation: Estimate the population mean weight using the sample mean weight. 2.Hypothesis Testing: Testing the claim that the population mean weight is 120 pounds.

6. Basic Concepts in Hypothesis Testing  Population: It consist of all the items or individuals about which you want to draw a conclusion.  Sample: A portion of a population selected for the analysis.  Parameter: It is a numerical measure that describes a characteristics of a population.  Statistics: A statistic is a numerical measure that describes a characteristic of a sample.

7. Basic Concepts in Hypothesis Testing (Cont)  Null Hypothesis (H 0 ): is a claim of “no difference in the population”.  Alternative Hypothesis (H a ): Claims “H 0 is false”

8. Example The problem: In the 1970s, 20–29 year old men in the U.S. had a mean μ body weight of 170 pounds. Standard deviation σ was 40 pounds. We test whether mean body weight in the population now differs. Null hypothesis H 0: μ = 170 (“no difference”) The alternative hypothesis can be either H a: μ > 170 (one-sided test) or H a: μ ≠ 170 (two-sided test)

9. Basic Concepts in Hypothesis Testing (Cont)  The Level of Significance: The level of significance is defined as the probability of rejecting a null hypothesis by the test when it is really true, which is denoted as α. That is, P (Type I error) = α.  Confidence Level: Confidence level refers to the possibility of a parameter that lies within a sp ecified range of values, which is denoted as C. The relationship between level of significance an d the confidence level is c=1−α.

10. The common level of significance and the corresponding confidence level are given below: The level of significance 0.10 is related to the 90% confidence level. The level of significance 0.05 is related to the 95% confidence level. The level of significance 0.01 is related to the 99% confidence level. The common level of significance and the corresponding confidence level are given below: The level of significance 0.10 is related to the 90% confidence level. The level of significance 0.05 is related to the 95% confidence level. The level of significance 0.01 is related to the 99% confidence level.

11. α Error & β Error Decision Reality H 0 - TrueH 0 - False Reject H 0 Type – 1 Error (α Error ) Correct Decision Accept H 0 Correct DecisionType – 2 Error (β Error)

12. One – Tail and Two – Tail Test

13. One-tailed test applies in situation where the researcher knows the direction the results should point. For example, when testing a new drug against a placebo, a researcher would want to know whether the new d rug is better than the placebo. On a family of normal distribution curves a one-tailed test can be in one di rection only, positive or negative. Two-tailed test applies in situation where the researcher does not know or is interested in both directions of the results. The two-tailed test is more commonly use than the one-tailed test. You must decide before you collect your data whether you are doing a one-tailed or two-tailed test.

14. Procedure For Testing Hypothesis There are five steps in the procedure of testing hypothesis. Step – 1: State the Null Hypothesis (H 0 ) and Alternate Hypothesis (H a ) Step – 2: Select appropriate statistic and level of significance Step – 3: State the decision rule Step – 4: Compute the appropriate test statistic and make the decision Step – 5: Compare the computed test statistic with critical value. Step – 6: Interpret the decision

15. Step – 1: State Ho and Ha Null Hypothesis: Statement about the value of a population parameter. Alternate Hypothesis: Statement that is accepted if evidence proves null hypothesis to be false.

16. Step – 2 Select Appropriate Statistics and Level of Significance Z – Statistics :  When Population σ, is known., and either the data is normally distributed or the sample size ( n > 30)  we use the Z-distribution (Z-statistic). T – Statistics:  When the population σ, is unknown, and either the data is normally distributed or the sample size is less th an 30 (n < 30)  we use the t-distribution (t-statistic).

17. Step - 3 State the decision rule The decision rules state the conditions under which the null hypothesis will be accepted or rejected. The critical value for the test-statistic is determined by the level of significance. The critical value is the value that divides the non-reject region from the reject region.

18. Step - 4 Compute the appropriate test statistics

19. Step - 5 Compare the computed test statistic with critical value. If the computed value is within the rejection region(s), we reject the null hypothesis; otherwise, we do not reject the null hypothe sis.

20. Step - 6 Interpret the Data Based on the decision in Step 4, we state a conclusion in the context of the original problem.

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