1 / 30

HYPOTHESIS TESTING

HYPOTHESIS TESTING. Prepared by: Paolo Bautista. Preliminaries. We wish to test whether a particular assumption/claim regarding the population is true or not. Null Hypothesis (H0) – original assumption Alternative Hypothesis (H1)

gusty
Download Presentation

HYPOTHESIS TESTING

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. HYPOTHESIS TESTING Prepared by: Paolo Bautista

  2. Preliminaries • We wish to test whether a particular assumption/claim regarding the population is true or not. • Null Hypothesis (H0) – original assumption • Alternative Hypothesis (H1) • Determine a critical value to determine whether or not to reject Ho HT : PLBautista

  3. Errors • Type I Error – reject H0 when in fact it is true • Type II Error – fail to reject H0 when it is false HT : PLBautista

  4. Steps in Hypothesis Testing • Write the null and alternative hypotheses. • Indicate the level of significance. • Determine the critical value/s. • Compute the test statistic. • Decide the conclusion of the test. HT : PLBautista

  5. HYPOTHESIS TESTING One Population Two Populations • One Mean • Case 1 • Case 2 • One Proportion • One Variance • Difference of Two Means • Case 1 to 3 • Paired Means • Difference of Two Proportions • Difference of Two Variances HT : PLBautista

  6. Testing for One Mean • Case 1: σ is known, or n ≥ 30 • Z-test will be used HT : PLBautista

  7. Testing for One Mean • The test statistic is given by HT : PLBautista

  8. Example 1 • A manufacturer of sports equipment has developed a new synthetic fishing line that he claims has a mean breaking strength of 8 kilograms with a standard deviation of 0.5 kilograms. Test the hypothesis that μ = 8 kg against the alternative that μ ≠ 8 kg if a random sample of 50 lines is tested and found to have a mean breaking strength of 7.8 kg. Use a 0.01 level of significance. HT : PLBautista

  9. Identify the proper hypotheses • The manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for a weekend is $600 or less. A member of the hotel’s accounting staff noticed that the total charges for guest bills have been increasing in recent months. The accountant will use a sample of weekend guest bills to test the manager’s claim. • The manager of an automobile dealership is considering a new bonus plan designed to increase sales volume. Currently, the mean sales volume is 14 automobiles per month. The manager wants to conduct a research study to see whether the new bonus plan increases sales volume. To collect data on the plan, a sample of sales personnel will be allowed to sell under the new bonus plan for a one-month period. HT : PLBautista

  10. Identify the proper hypotheses • A production line operation is designed to fill cartons with laundry detergent to a mean weight of 32 ounces. A sample of cartons is periodically selected and weighed to determine whether underfilling or overfilling is occurring. If the sample data lead to a conclusion of underfilling or overfilling, the production line will be shut down and adjusted to obtain proper filling. • Because of high production-changeover time and costs, a director manufacturing must convince management that a proposed manufacturing method reduces costs before the new method can be implemented. The current production method operates with a mean cost of $220 per hour. A research study will measure the cost of the new method over a sample production period. HT : PLBautista

  11. Case 2: σ unknown, AND n < 30 • t-test will be used • The t-values have n – 1 degrees of freedom • The test statistic is given by HT : PLBautista

  12. Example 2 • Test the hypothesis that the average content of containers of a particular lubricant is 10 liters if the contents of a random sample of 10 containers are 10.2, 9.7, 10.1, 10.3, 10.1, 9.8, 9.9, 10.4, 10.3, and 9.8 liters. Use a 0.01 level of significance and assume that the distribution of contents is normal. HT : PLBautista

  13. Testing for One Proportion • Z-test will be used • The test statistic is given by HT : PLBautista

  14. Example 3 • A commonly prescribed drug on the market for relieving nervous tension is believed to be only 60% effective. Experimental results with a new drug administered to a random sample of 100 adults who were suffering from nervous tension showed that 70 received relief. Is this sufficient evidence to conclude that the new drug is superior to the one commonly prescribed? Use a 0.05 level of significance. HT : PLBautista

  15. Testing for One Variance • A chi-square test will be used • The test statistic is given by HT : PLBautista

  16. Example 4 • A manufacturer of car batteries claims that the life of his batteries has a variance equal to 0.81 years. If a random sample of 10 of these batteries have a variance of 1.44 years, is there evidence that the variance exceeds 0.81 a year? Use a 0.05 level of significance HT : PLBautista

  17. Testing the Difference of Two Means • Case 1: • Z-test will be used • The test statistic is given by: HT : PLBautista

  18. Example 5 • A manufacturer claims that the average tensile strength of thread A exceeds the average tensile strength of thread B by less than 12 kilograms. To test this claim, 50 pieces of each type of thread are tested under similar conditions. Type A thread had an average tensile strength of 86.7 kilograms with a standard deviation of 6.28 kilograms, while type B thread had an average tensile strength of 77.8 kilograms with a standard deviation of 5.61 kilograms. Test the manufacturer’s claim using a 0.05 level of significance. HT : PLBautista

  19. Case 2: σ1=σ2 unknown, AND n1<30 and n2<30 • t-test will be used. • The test statistic is given by • The degrees of freedom to be used is HT : PLBautista

  20. Example 6 • A course in mathematics is taught to 12 students by the conventional classroom procedure. A second group of 10 students was given the same course by means of programmed materials. At the end of the semester the same examination was given to each group. The 12 students meeting in the classroom made an average grade of 85 with a standard deviation of 4, while the 10 students using programmed materials made an average of 81 with a standard deviation of 5. Test the hypothesis that the two methods of learning are equal using a 0.10 level of significance. Assume the population to be approximately normal with equal variances. HT : PLBautista

  21. Case 3: σ1≠σ2 unknown, AND n1<30 and n2<30 • t-test will be used • The test statistic is given by • The degrees of freedom is given by HT : PLBautista

  22. Example 7 • An improved manufacturing process is developed. The quality-control tests show that the old process has an average score of 12.8 with a standard deviation of 2.5 based on a sample of 8 observations, while the new process shows an average score of 14.2 with a standard deviation of 1.6 based on a sample of 10 observations. Use a 0.05 level of significance to determine whether there has been a significant increase in the average scores of the new process, assuming unequal variances. HT : PLBautista

  23. Paired Observations • t-test will be used • The test statistic is given by • The degrees of freedom to be used is n – 1, where n is the number of pairs HT : PLBautista

  24. Example 8 • To determine whether membership in a fraternity is beneficial or detrimental to one’s grades, the following grade-point averages were collected over a period of 5 years: • Assuming the populations to be normal, test at the 0.05 level of significance whether membership in a fraternity is detrimental to one’s grades. HT : PLBautista

  25. Testing for Two Proportions • Z-test will be used • The test statistic is given by HT : PLBautista

  26. Example 9 • A vote is to be taken among the residents of a town and the surrounding county to determine whether a civic center will be constructed. To determine if there is a significant difference in the proportion of town voters and county voters favoring the proposal, a poll is taken. If 120 of 200 town voters favor the proposal and 240 of 500 county residents favor it, would you agree that the proportion of town voters favoring the proposal is higher than the proportion of county voters? Use a 0.025 level of significance. HT : PLBautista

  27. Testing for Two Variances • F-test will be used HT : PLBautista

  28. Example 10 • Verify if the assumption of equal variance in Example 6 is valid by conducting a test of hypothesis. Use a 0.10 level of significance. HT : PLBautista

  29. p-value approach • The p-value is the probability that we obtain the sample data, assuming the null hypothesis is true. • We reject Ho if the p-value is small. • Usually, we use the level of significance as a comparison value. HT : PLBautista

  30. Estimation and HT HT : PLBautista

More Related