Hypothesis Testing Review Questions, Exams of Probability and Statistics

Download Hypothesis Testing Review Questions and more Exams Probability and Statistics in PDF only on Docsity! Hypothesis Testing: Review Questions (Use a 5% significance level unless indicated otherwise.) 1. You want to test the hypothesis that a coin is fair. You flip the coin 100 times. What do you conclude if 65 heads occur, 56 heads, 38 heads. 1. Riverboat Gambling sets up on the Poughkeepsie water front. The most popular game is coin flipping (Heads the house wins, tails the player wins.) You are appointed to check the fairness of this game. Suppose that you observed 100 flips of the coin. What do you conclude if 65 heads occur. 56 heads, 38 heads. 2. You want to test the hypothesis that a coin is a fair coin. The following test is proposed: The coin is flipped 100 times. If the number of heads is greater than 60 or less than 40 it is concluded that the hypothesis of fairness is rejected. What is the significance level of this test 3. A firm is testing a new design for a light bulb. The old design bulbs produce bulbs with lasted 2000 hours on the average with a standard deviation of 400 hours. 100 new bulbs are produced and tested. The average life is 1270. Would you conclude that the new design is better. 4. Redo 3 assuming that the standard deviation is unknown, but that the sample standard deviation is 400 hours. 5. Redo 4 and 5 with a two sided test. 6. A firm is testing a new production process. Under the old method the proportion of defective units was .20. The following test is used. One hundred test units are produced and inspected. 12 are defective. Would you conclude that the new process is better. 7. Suppose we redesign the test in question 7. We choose a cri tical value of the number of defective units. If the number of defective units is less than that critical value we reject the null hypothesis. What should the critical value be if the significance level is to be .01 8. 20% of the jury age population in a certain Alabama county are African-Americans. However only 30 African-Americans appear among the last 400 persons called for jury duty. Does this evidence suggest that the jury selection process discriminates against African-Americans? Clearly state the null and alternative hypotheses and the results of the hypothesis test. Use a 5% significance level. 9. A sample of size 25 is drawn from a normal population. The sample mean is 72 and the sample variance is 64. a) Test the hypothesis that the population mean is 68 against the alternative hypothesis that the population mean is greater than 68. b) How would your answer change if the alternative hypothesis was that the population mean was different than 68. 10. A cereal manufacturer claims that the average amount of sugar in a one pound box of cereal is at most 50 grams with a standard deviation of 10 grams. In order to test that claim the following test is defined. A sample of 25 boxes of cereal is selected and the mean amount of sugar, , is calculated. If the null hypothesis is rejected. What should the value of be if the significance level of the test is to be 5%. (You should clearly state what the null and alternative hypotheses are.) 12. A tobacco company claims that its cigarettes contain an average of less than one milligrams of nicotine per cigarette. The standard deviation of the amount of nicotine contained in a cigarette is 0.5 milligrams. In order to test the claim the following test is carried out: A sample of 25 cigarettes is selected and tested. If the average amount of nicotine in the sampled cigarettes exceeds 1.1 miligrams the companies claim is rejected. a) What are the null and alternative hypotheses for this test. Is this a one sided or a two sided test. Why is this appropriate. b) Find the significance level of this test. c) How many cigarettes should be sampled if the significance level of this test is to be .01? 13. A firm is testing a new production process. Under the old method the proportion of defective units was .20. The following test is used. One hundred units are produced with the new process and inspected. If 12 or fewer are defective it is concluded that the new process is superior to the old process. a) What is the significance level of the test. b) How many chips should you produce if the significance level of this test is to be .01. 14. A firm which produces SAT preparation courses claims that 80% of the persons who take their course achieve a score of at least 600 on the math SAT. In order to test that claim you construct the following test. A random sample of 100 persons who have taken the test is selected and the proportion P who achieved a math score of 600 is calculated. If the proportion achieving that score is less than a critical value Pc the claim of the firm is rejected. What should Pc be if the significance level of this test is to be .01? 15. You are the president of a firm which manufactures hard drives for computers. You are considering coming out with a new model of hard drive. The model which you are now producing fails on the average 1% of the time in the first month. Your chief engineer assures you that this model will fail less frequently that. The following test is designed. 1000 hard drives are produced and tested. If less than 5 fail in the first month it is concluded that the new model is superior. Find the significance level of the test. How would the following information affect your choice of a significance level. A) The chief engineer is willing to stake his reputation on the fact that the new drive is superior, and you have reason to trust his judgement. B) The changover to the production of the new model is very costly. 16. Two makes of typewriter are to be tested. Six typists are randomly chosen and tested on machine A. Six more typists are tested on typewriter B. The results are typewriter A typewriter B 60 52 82 60 70 68 76 70 90 80 82 74 a) Would you conclude that one typewriter is faster. You may assume that typing speeds are normally distributed. b) How would your answer change if the two machines were tested with the same typists. (Hint:this is a paired sample. See Webster, 9.7) 17. In order to investigate whether men or women are more likely to favor gun control independent samples of 100 men and 100 women are polled. The results are that the proportion of men favoring gun control is .60 and the proportion of women is .70. Test the hypothesis that there is no difference between of men and women supporting gun control 18. Samples of size 100 and 200 are drawn respectively from two normal populations A and B. The results are A: sample size = 100, sample mean =64, sample variance = 30; B: sample size = 200, sample mean = 67, sample variance = 49. Test the hypothesis that the population means are the same.