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  1. 1. Hypothesis Testing
  2. 2. Introduction <ul><li>A statistical hypothesis is an assumption about an unknown population parameter. </li></ul><ul><li>It is a well defined procedure which helps us to decide objectively whether to accept or reject the hypothesis based on the information available from the sample. </li></ul><ul><li>In statistical analysis, we use the concept of probability to specify a probability level at which a researchers concludes that the observed difference between the sample statistics and population parameter is not due to chance. </li></ul>
  3. 3. Hypothesis Testing Procedure
  4. 4. Step 1: - Set Null and Alternative Hypothesis <ul><li>The null hypothesis is denoted by Ho, is the hypothesis which is tested for the possible rejection under the assumption that it is true. </li></ul><ul><li>Theoretically, Ho is set as no difference considered true, until and unless it is proved wrong by the collected sample data. </li></ul><ul><li>The alternative hypothesis is denoted by H1 or H α , is a logical opposite of the Ho. </li></ul>
  5. 5. Step 2: - Determine the appropriate Statistical Test <ul><li>After setting he hypothesis, the researches has to decide on an appropriate statistical test that will be tested for the statistical analysis. </li></ul><ul><li>The statistic used in the study (mean, proportion, variance etc.) must also be considered when a researchers decides on appropriate statistical test, which can be applied for hypothesis testing in order to obtain the best results. </li></ul>
  6. 6. Step 3: - set the level of significance <ul><li>The level of significance is denoted by α is the probability, which is attached to a null hypothesis, which may be rejected even when it is true. </li></ul><ul><li>The level of significance also known as the size of the rejection region or the size of the critical region. </li></ul><ul><li>Level of significance must be determined before we draw samples, so that the obtained result is free from the bias of a decision maker. </li></ul><ul><li>0.01, 0.05, 0.010 </li></ul>
  7. 7. Step 4: - Set the decision Rule <ul><li>If the computed value of the test statistic falls in the Next step is to establish a critical region , which is the area under the normal curve . These regions are termed as acceptance region (when the Ho is accepted) and the rejection region or critical region. </li></ul><ul><li>acceptance region , the null hypo is accepted . </li></ul><ul><li>Otherwise Ho is rejected. </li></ul>
  8. 8. Step 5: - Collect the sample data <ul><li>In this stage data are collected and appropriate sample statistics are computed. </li></ul><ul><li>The first 4 steps should be completed before collecting the data for the study. </li></ul>
  9. 9. Step 6: - Analyze the data <ul><li>In this step the researcher has to compute the test statistic. This involves selection of appropriate probability distribution for a particular test. </li></ul><ul><li>For Example- When the sample is small, then t-distribution is used. If sample size is large then use Z-test. </li></ul><ul><li>Some commonly used testing procedures are F, t, Z, chi square. </li></ul>
  10. 10. Step 7: - Arrive at a statistical conclusion <ul><li>In this step the researcher draw a conclusion. A statistical conclusion is a decision to accept or reject a Ho. This depends whether the computed statistic falls in the acceptance region or rejection region. </li></ul>
  11. 11. Critical Region <ul><li>The critical region (or rejection region ) is the set of all values of the test statistic that cause us to reject the null hypothesis. </li></ul>
  12. 12. Significance Level <ul><li>The significance level (denoted by  ) is the probability that the test statistic will fall in the critical region when the null hypothesis is actually true. Common choices for  are 0.05, 0.01, and 0.10. </li></ul>
  13. 13. Critical Value <ul><li>A critical value is any value separating the critical region (where we reject the H0) from the values of the test statistic that does not lead to rejection of the null hypothesis, the sampling distribution that applies, and the significance level  . </li></ul>
  14. 14. F-TEST
  15. 15. <ul><li>The name was coined by George W. Snedecor , in honour of Sir Ronald A.isher . </li></ul><ul><li>Any statistical test in which the test statistic has an F-distribution under the null hypothesis. </li></ul><ul><li>It is most often used when comparing statistical models that have been fit to a data set, in order to identify the model that best fits the population from which the data were sampled. </li></ul><ul><li>The F-test is designed to test if two population variances are equal. It does this by comparing the ratio of two variances. So, if the variances are equal, the ratio of the variances will be 1. </li></ul>
  16. 16. CALCULATION OF F-TEST <ul><li>The F-tests arise by assuming decomposition of variability while collecting data with sums of squares. </li></ul><ul><li>These sums of squares are developed together such that the statistics tends greater in a condition when the null hypothesis is false. </li></ul><ul><li>When using the F -test, you again require a hypothesis to compare standard deviations. That is, you will test the null hypothesis H o: σ 12 = σ 22 against an appropriate alternate hypothesis. </li></ul>
  17. 17. <ul><li>You calculate the value of the F-test as the ratio of the two variance where s 12 ≥ s 22, so that F ≥ 1. The degrees of freedom for the numerator and denominator are n 1-1 and n 2-1, respectively . </li></ul><ul><li>The degrees of freedom for the numerator and denominator are n 1-1 and n 2-1, respectively. </li></ul><ul><li>As with the t -test, you compare Fcalc to a tabulated value Ftab , to see if you should accept or reject the null hypothesis. </li></ul>
  19. 19. XYZ constructions is a leading company in the construction sector in Delhi . It wants to construct flats in two areas, Indrapuram & Pritampura . The company wants to estimate the amount that customers are willing to spend on purchasing a flat in the two areas . It randomly selected 21 potential customers from Pritampura and 27 from Indrapuram and posed the question, “how much are you willing to spend on a flat?” The data collected from the two areas is shown in table below.
  20. 20. The company assumes that the intention to purchase of the customers is normally distributed with equal variance in the two areas taken for the study. On the basis of the samples taken for the study, estimate the difference in population means taking 95% as the confidence level.
  21. 21. Proposed Exp. On flats by customers from Indrapuram (in thousand Rs.) 125 165 130 170 126 130 127 145 150 130 135 140 140 150 160 160 120 140 150 145 155 165 145 140 165 135 130 140 145 160 155 150 145 160 155 150 170 160 190 145 180 190 170 180 160 185 165 135 185 Proposed Exp. On flats by customers from Pritampura (in thousand Rs.)