![Analyze sample data.
• Using sample data, we calculate the standard
deviation (σ) and compute the z-score test
statistic
• (z).σ = sqrt[ P * ( 1 - P ) / n ]
• σ = sqrt [(0.8 * 0.2) / 100]
• σ = sqrt(0.0016) = 0.04
• z = (p - P) / σ = (.73 - .80)/0.04 = -1.75
• where P is the hypothesized value of population
proportion in the null hypothesis, p is the sample
proportion, and n is the sample size.](https://image.slidesharecdn.com/10-hypothesisteesting-210303063244/85/hypothesis-teesting-15-320.jpg)
hypothesis teesting
- 1. Methods of Hypothesis Testing Dr. Kshitija Gandhi PHD, MPHIL, MCOM,MBA,UGC NET Vice Principal Pratibha College of Commerce and Computer studies
- 2. Traditional Method Step 1 Identify the Null Hypothesis and the Alternative Hypothesis Step 2 Identify α (Level of Significance) Step 3 Find the critical value(s) Step 4 Find the test statistic Step 5 Draw a graph and label the test statistic and critical value(s) Step 6 Make a decision to reject or fail to reject the null hypothesis · Reject H0 - The test statistic falls within the critical region. · Fail to Reject - Test statistic does not fall within the critical region.
- 3. P-Value Method Fail to reject H0: if p-value > α Reject H0:if p-value ≤ α Two Tailed Test: p-value is twice the area bounded by the test statistic Make a decision to reject or fail to reject the null hypothesis: Right Tail Test: p-value is the area to the right of the test statistic. Left Tail Test: p-value is the area to the left of the test statistic. P-value is the area determined as follows
- 4. Conclusion All hypothesis tests are conducted the same way. The researcher states a hypothesis to be tested, formulates an analysis plan Analyzes sample data according to the plan, Accepts or rejects the null hypothesis, based on results of the analysis.
- 5. State the Hypotheses Every hypothesis test requires the analyst to state a null hypothesis and an alternative hypothesis. The hypotheses are stated in such a way that they are mutually exclusive. That is, if one is true, the other must be false; and vice versa.
- 6. Formulate an Analysis Plan The analysis plan describes how to use sample data to accept or reject the null hypothesis. It should specify the following elements. Significance level. Often, researchers choose significance levels equal to 0.01, 0.05, or 0.10; but any value between 0 and 1 can be used.
- 7. Formulate an Analysis Plan • Test method. Typically, the test method involves a test statistic and a sampling distribution. • Computed from sample data, the test statistic might be a mean score, proportion, difference between means, difference between proportions, z-score, t statistic, chi-square, etc. • Given a test statistic and its sampling distribution, a researcher can assess probabilities associated with the test statistic. If the test statistic probability is less than the significance level, the null hypothesis is rejected.
- 8. Analyze sample data. Using sample data, perform computations called for in the analysis plan. Test statistic. When the null hypothesis involves a mean or proportion, use either of the following equations to compute the test statistic. Test statistic = (Statistic - Parameter) / (Standard deviation of statistic) Test statistic = (Statistic - Parameter) / (Standard error of statistic) • where Parameter is the value appearing in the null hypothesis, • Statistic is the point estimate of Parameter. • As part of the analysis, you may need to compute the standard deviation or standard error of the statistic. Previously, we presented common formulas for the standard deviation and standard error. When the parameter in the null hypothesis involves categorical data, you may use a chi-square statistic as the test statistic. Instructions for computing a chi-square test statistic are presented in the lesson on the chi-square goodness of fit test. • P-value. The P-value is the probability of observing a sample statistic as extreme as the test statistic, assuming the null hypothesis is true.
- 9. Analyze sample data. • When the parameter in the null hypothesis involves categorical data, use a chi-square statistic as the test statistic. Instructions for computing a chi-square test statistic are presented in the lesson on the chi- square goodness of fit test. • P-value. The P-value is the probability of observing a sample statistic as extreme as the test statistic, assuming the null hypothesis is true.
- 10. Interpret the Results If the sample findings are unlikely, given the null hypothesis, the researcher rejects the null hypothesis. Typically, this involves comparing the P-value to the significance level, and rejecting the null hypothesis when the P-value is less than the significance level.
- 11. Problem 1: Two-Tailed Test • The CEO of a large electric utility claims that 80 percent of his 1,000,000 customers are very satisfied with the service they receive. To test this claim, the local newspaper surveyed 100 customers, using simple random sampling. Among the sampled customers, 73 percent say they are very satisfied. • Based on these findings, can we reject the CEO's hypothesis that 80% of the customers are very satisfied? • Use a 0.05 level of significance.
- 12. Solution The solution to this problem takes four steps: State the hypotheses Formulate an analysis plan Analyze sample data Interpret results
- 13. State the Hypotheses • The first step is to state the null hypothesis and an alternative hypothesis. • Null hypothesis: P = 0.80 • Alternative hypothesis: P ≠ 0.80 • Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample proportion is too big or if it is too small.
- 14. Formulate an Analysis Plan For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.
- 15. Analyze sample data. • Using sample data, we calculate the standard deviation (σ) and compute the z-score test statistic • (z).σ = sqrt[ P * ( 1 - P ) / n ] • σ = sqrt [(0.8 * 0.2) / 100] • σ = sqrt(0.0016) = 0.04 • z = (p - P) / σ = (.73 - .80)/0.04 = -1.75 • where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.
- 16. Analyze sample data. • Since we have a two-tailed test, the P-value is the probability that the z-score is less than -1.75 or greater than 1.75. • We use the Normal Distribution Calculator to find P(z < -1.75) = 0.04, and P(z > 1.75) = 0.04. Thus, the P-value = 0.04 + 0.04 = 0.08.
- 17. Interpret Results • Since the P-value (0.08) is greater than the significance level (0.05), we cannot reject the null hypothesis.