Name: ___________________________________ Date: ______________________ Introduction to Hypothesis Testing and One Population Hypothesis Testing 1.Which hypothesis does the researcher hope to reject, H0 or HA? 2. What is the denominator of the one-sample z statistic? 3. A coffee vending machine, tested n= 16 times, yielded a mean cup fall of 6.2 oz with a standard elevation of 0.15 oz. Assuming that these data can be look upon a random sample from a normal population, test the null hypothesis µ= 6.0 oz against the alternative hypothesis µ>6.0 oz at the 0.01 level of significance. 4. A new tranquilizer given to n=16 patients reduced their pulsed rate on the average by 4.36 beat per minute with a standard deviation of 3.06 per min. Assuming that such data can be looked upon as a random sample from a normal population use the 0.10 level of significance to test the pharmaceutical company’s claim that on the average its new tranquilizer reduces a patients pulse rate by 4.50 beats per minute. 5. Misconceived hypotheses. What is wrong with each of these statements? a. H0: µ = 100 vs. H1: µ 110 b. H0: = 100 vs. H1: < 100 6. Lithium carbonate is a drug used to treat bipolar mental disorders. The average dose in well-maintained patients is µ = 1.3 mEq/L ( = 0.3 mEq/L). A random sample of 25 patients on lithium demonstrates a mean lithium level =1.4 mEq/L. a) Conduct a one sample z test to see if the observed difference is significant. [Use a two-sided alternative, as improper dosing would include both under- and over-dosing.] b) Are the results significant at alpha = 0.05? Are they significant at alpha = 0.10? 7. According to the norms established for reading comprehension test, eight grader should have an average of 83.2 with the standard deviation of 1.6. A district superintendent feels that the eight graders in his district are above average in reading comprehension, but he 01 addresses this objection. A random of 16 applicants took the typing test and an average speed of 62 words per minute with a standard deviation of 8 words per minute was obtained. Test the claim that the applicants performance is below the standard at 0. A critic notes that only 13 patients were studied so the observed drop could have occurred merely by chance. What can he conclude. A sample of 50 pieces is drawn with an average weight of 22g and SD of 15. will you decide to harvest your stock? OF Innocent Committed crime the . An expert typist can type 65 words per minute.9 words per minute.01). Use α= 0. Fill in the table below.2 words per minute with a standard deviation of 7.01 level of significance and he chooses a random sample of 45 eight graders from his district.05. 9. Explain how the statistic P = 0.lacks proof. A jury having heard the evidence in a criminal case is debating whether or not to render a verdict of guilty or not guilty. Because it is worse to convict an innocent person of a crime they did not commit than to let a guilty person go free. typed on the average of 78.2 against a suitable alternative at 0. A random sample of 12 graduates of BSIT-Comp. test the null hypothesis µ= 80 words per minute against the alternative hypothesis µ< 80 words per minute. Which of these decisions is analogous to a type I error. if the sample mean is 86. A cross-over trial of 13 diabetics compared cholesterol levels while on a moderate-fiber diet and while on a high-fiber diet. This is analogous to assumption or retaining H0 in a statistical hypothesis test. Tech. A stock of tilapia will only be harvested if the average body weight of the tilapia is greater than 20g. Assuming that such data can be looked upon as a random sample from a normal population. The study concluded that the high-fiber diet reduced very-low-density lipoprotein cholesterol by 12.05 level of significance. and which is analogous to a type II error? TRUTH DECISION JURY Not Guilty Guilty 11. The criminal justice analogy. So he decided to test the null hypothesis µ= 83. of CSCST-MC. for graduates of this secretarial school. 10.7? 8. 12.5% (P = 0. each case begins with an assumption of innocence. Using a test of hypothesis at the 1% level of significance. According to the results of 1998 National Demographic Survey of the National Statistics Office. Among 10.000 school children.87 pCi/L. is there enough evidence that the proportion of women aged 20-49 years old who had sexual intercourse by age 15 would exceed 3%? 16. 17. Blood tests are preformed on 100 female Filipinos in this age range rendered a sample mean cholesterol level of 181.13. We want to compare fasting serum cholesterol levels of Filipino women to that of the other foreign women. A poll survey in Cebu City was conducted in order to determine what percentage of the voting population would favor Candidate X in the upcoming 2010 national election.059 women aged 20-49 years old 288 had sexual intercourse by age 15. Assume the cholesterol levels in 20.39 pCi/L and a standard deviation of 0. Conduct a test of hypothesis to determine whether Filipino women have lower average cholesterol levels than their foreign counterparts.52 mg/dl and standard deviation of 40 mg/dl. is there any evidence that the proportion of voters that favors Candidate X exceeds 40%? 14. so samples of water are assumed safe unless there is evidence to the contrary. Test the hypothesis that the average daily expenditure of the sample is lower than the population. Samples of 60 families have an average daily expenditure of Php195. However. A random sample of 25 specimens of water from a city's water supply gave a mean of 5. with a standard deviation of Php15. Using a 5% level of significance. . Of these 500 school children. is their evidence that the proportion of moderately and severely underweight children is 20%? 15. The results of the survey revealed that out of 88 respondents.01 level of significance. out of 11. At 5% level of significance. it is well known that even safe water has occasional hot spots that eventually get diluted. namely an average of 5 Pico curies per litre (pCi/L) or less. Use 0. 18. Of prime concern is the possibility that release of these byproducts into the environment may contaminate the freshwater supply. Show all hypothesis testing steps. 500 of them are randomly selected for a survey on nutritional status among school age children.to 39-years old women in other foreign countries is normally distributed with mean µ = 190 mg/dl. The average daily expenditure of food of a poor family is Php200. 35 people would vote for Candidate X. In some mining operations. 91 are found to be moderately and severely underweight children. a byproduct of the processing is mildly radioactive. There are strict regulations for the maximum allowable radioactivity in supplies of drinking water. At 5% level of significance. c. More than one of the above is true. Would you reject the null hypothesis at the 10% significance level? c. diagnosing a diseased person as diseased. and your null hypothesis is that the mean of the population is equal to 15. c. For nos. c. 22. At 1% significance level? 20. d. What level (p-value) is x =13 . d. Use µ for a claim about a mean and π for a claim about a proportion. not billing the patient. at what significance level would you question his assertion? 21. Identify the test as being two-tailed. b. d. Identify the null hypothesis Ho. diagnosing a diseased person as healthy. The level of significance is the probability of a Type I error. What is the appropriate null hypothesis? b. If a politician for the upcoming 2010 national elections claims that at least 67% of the voters approve of his record. f. When conducting a test of hypothesis.a. b.5 based on a sample of size 200 significant? b. or right-tailed. None of the above is true. e. a. If the standard deviation is known to be equal to 12. If the null hypothesis is that a person is healthy. a. You reject H0 if p-value is greater than the level of significance. a Type II error entails a. What is the corresponding alternative hypothesis? 19. e. left-tailed. 23-26. Identify the type II error for this test. For the next four exercises. but only 110 out of 180 voters in a survey approve of his record. The probability of a Type I error depends on the alternative hypothesis. diagnosing a healthy person as diseased. At 5% significance level? d. which of the following is a true statement? a. e. assume that a hypothesis test of the given claim will be conducted. Express the claim in symbolic form. diagnosing a healthy person as healthy. Identify the type I error for this test. Identify the alternative hypothesis HA. . b. The president of a Car Park is trying to plan a sales campaign targeted at car owners who are ready to buy a different car. A survey of 506 high-school students showed that 268 of them did not know that the Philippines was under the .01 years and the standard deviation is 3. In a study of factors affecting hypnotism. 27. 26. The Laban Party standard bearer claims that he is currently favored by more than one-half of his constituency. be sure to address the original claim. Test the claim that fewer than 10% of cars on the road have a design that benefits from higher octane gasoline.0. Department of Health claims that a pharmaceutical company makes cold capsules that contain amounts of acetaminophen with a mean different from the 500 mg amount indicated on the label. then the curriculum should be revised to correct that deficiency.g. h.05 level of significance to test the claim that with scanners. The Land Transportation Office would like to know if motorists are being seduced by ads to buy higher octane gas than is useful. do scanners appear to help consumers avoid overcharges? 30.74 years. For these sample ratings.234 items were checked and 20 of them were found to be overcharges. 25. Use a 0. test the claim that this sample comes from a population with a mean rating of less than 10. A poll of 100 randomly selected car owners revealed that the mean length of time that they plan to keep their cars is 7. be sure to address the original claim. Mr.5 year.01 level of significance. Test the claim of the sales manager. 24. the mean is 8. Use a 0. In a study of store checkout scanners. State the conclusion in non-technical terms. 1. visual analogue scale (VAS) sensory ratings were obtained for 16 subjects. Based on these results. 28. Assume that the conclusion is failure to reject the null hypothesis. who authoritatively states that the mean length of time all car owners plan to keep their cars is less than 7. State the conclusion in non-technical terms. 23.05 level of significance.33 while the standard deviation is 1. 29. 1% of sales are overcharged. At the 0.96. X is a high-school history teacher who says that if students are not aware of the Martial Law. Assume that the conclusion is to reject the null hypothesis. The Department of Education claims that over 2% of all adults are enrolled in school full-time. Martial Law for more than 10 years. test the claim that most (more than 50%) students don’t know what happened during the Martial Law.05 level of significance. should Mr. Abad Santos seek revisions to the curriculum? . Using the sample data and a 0. Based on these results.
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