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1 9_1&9_2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Express the null hypothesis. 1) Which could be the null hypothesis for the true proportion of fireflies unable to produce light? 1) A) H: p <.12 B) H: p.12 C) H: p =.12 D) H: p.12 E) H: p >.12 Examine the given statement, then identify whether the statement can be the null hypothesis, the alternative hypothesis or neither. 2) The mean income of workers who have majored in history is less than \$25,. 2) A) Null hypothesis B) Alternative hypothesis C) Neither 3) The more college courses a person has will lead to a higher salary. 3) A) Null hypothesis B) Alternative hypothesis C) Neither 4) The mean µ = ) A) Null hypothesis B) Alternative hypothesis C) Neither Determine the null and alternative hypotheses. 5) In the past, the mean running time for a certain type of radio battery has been 9.6 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has changed as a result. A) H : µ = 9.6hours : µ > 9.6 hours B) H : µ > 9.6hours : µ > 9.6 hours C) H : µ 9.6 hours : µ = 9.6hours D) H : µ = 9.6 hours : µ 9.6 hours E) H : µ 9.6 hours : µ = 9.6 hours 5) 1

2 6) A manufacturer claims that the mean amount of cola in its 16 ounce bottles is 16.1 ounces. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this. A) H : µ = 16.1 ounces : µ > 16.1 ounces B) H : µ < 16.1 ounces : µ > 16.1 ounces C) H : µ = 16.1 ounces : µ < 16.1 ounces D) H : µ = 16.1 ounces : µ 16.1 ounces E) H : µ < 16.1 ounces : µ = 16.1 ounces 6) 7) A health insurer has determined that the "reasonable and customary" fee for a certain medical procedure is \$12. They suspect that the average fee charged by one particular clinic for this procedure is higher than \$12. The insurer wants to perform a hypothesis test to determine whether their suspicion is correct. A) H : µ = \$12 : µ \$12 B) H : µ = \$12 : µ < \$12 C) H : µ > \$12 : µ < \$12 D) H : µ > \$12 : µ = \$12 E) H : µ = \$12 : µ > \$12 7) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 8) Suppose the claim is in the alternate hypothesis. What form does your conclusion take? Suppose the claim is in the null hypothesis. What form does your conclusion take? 8) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Select the most appropriate answer. 9) Which of the following would be an appropriate alternative hypothesis? 9) A) The population proportion is less than.41. B) The sample proportion is not equal to.41. C) The sample proportion is equal to.41. D) The population proportion is equal to.41. E) The sample proportion is less than.41. 2

3 Determine the null and alternative hypotheses. 1) In 199, the average duration of long-distance telephone calls originating in one town was 7.2 minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 199 mean of 7.2 minutes. A) H : µ = 7.2 minutes : µ 7.2 minutes B) H : µ 7.2 minutes : µ = 7.2 minutes C) H : µ = 7.2 minutes : µ > 7.2 minutes D) H : µ < 7.2 minutes : µ > 7.2 minutes E) H : µ = 7.2 minutes : µ 7.2 minutes 1) 11) A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz. 11) A) H: µ = 14 H1: µ 14 B) H: µ = 14 H1: µ > 14 C) H: µ = 14 H1: µ 14 D) H: µ = 14 H1: µ 14 E) H: µ = 14 H1: µ < 14 Find the P-value for the indicated hypothesis test. 12) A medical school claims that more than 28% of its students plan to go into general practice. It is found that among a random sample of 13 of the school's students, 39% of them plan to go into general practice. Find the P-Value for a test of the school's claim. A).26 B).28 C).1635 D).3461 E) ) In a sample of 47 adults selected randomly from one town, it is found that 9 of them have been exposed to a particular strain of the flu. Find the P-value for a test of the claim that the proportion of all adults in the town that have been exposed to this strain of the flu is 8%. A).8 B).24 C).262 D).48 E) ) 13) Select the most appropriate answer. 14) Given Ha p. What is the P-value if the test statistics is calculated to be z = -.12? 14) A).12 B).9 C).1 D).95 E).5 15) Given Ha p. What is the P-value if the test statistics is calculated to be z =.58? 15) A).11 B).56 C).5 D).22 E).28 3

4 Explain what the P-value means in the given context. 16) A state university wants to increase its retention rate of 4% for graduating students from the previous year. After implementing several new programs during the last two years, the university reevaluates its retention rate and comes up with a P-value of.75. What is reasonable to conclude about the new programs using =.5? A) There is a 92.5% chance of the new programs having no effect on retention. B) We can say there is a 7.5% chance of seeing the new programs having no effect on retention in the results we observed from natural sampling variation. There is no evidence the new programs are more effective, but we cannot conclude the new programs have no effect on retention. C) We can say there is a 7.5% chance of seeing the new programs having an effect on retention in the results we observed from natural sampling variation. We conclude the new programs are more effective. D) There's only a 7.5% chance of seeing the new programs having no effect on retention in the results we observed from natural sampling variation. We conclude the new programs are more effective. E) There is a 7.5% chance of the new programs having no effect on retention. 17) A weight loss center provided a loss for 72% of its participants. The center's leader decides to test a new weight loss strategy to see if it's better and receives a P-value of.23. What is reasonable to conclude about the new strategy using =.1? A) There is a 77% chance of the strategies being equally effective. B) There's only a 23% chance of seeing the strategies being equally effective in the results we observed from natural sampling variation. We conclude the new strategy is more effective. C) We can say there is a 23% chance of not seeing the strategies being equally effective in the results we observed from natural sampling variation. We conclude the new strategy is more effective. D) We can say there is a 23% chance of seeing the strategies being equally effective in the results we observed from natural sampling variation. There is no evidence the new strategy is more effective, but we cannot conclude the strategies are equally effective. E) There is a 23% chance of the strategies being equally effective. 16) 17) For the given sample data and null hypothesis, compute the value of the test statistic, z 18) A claim is made that the proportion of children who play sports is less than.5, and the sample statistics include 1933 subjects with 3% saying that they play a sport. A) B).5 C) D) E) ) In a school district with 1, high school students, 12 students completed a special class designed to improve their math skills. 78 of these scored better than the district-wide median on a standardized math exam. Does the special class have some value? The hypotheses are H : p =.5, : p >.5, where p is the proportion of all those taking the special class who score better than the district-wide median. A) B) C) 78 D) E) ) 19) 2) Out of 199 observations, 5% were successes. H: p =.43. 2) A) B) C) D).43 E).2 4

5 21) A radio show producer believes that a new proposed format would be preferred by only 2% of their current listeners. A survey of 1 current listeners showed that 17% favored the new format. Does the producer know his business? H: p =.2 A) -.99 B).17 C) D) E) ) Select the most appropriate answer. 22) A researcher claims that less than 2% of American adults are allergic to pollen. In a random sample of 1 adults, 15% indicate that they have such an allergy. Calculate the test statistic z for the population proportion. A) 1.25 B) C) 1.96 D) E) None of the above. 23) A research company claims that more than 55% of American regularly watch FOX News Watch. You decide to test this claim and ask a random sample of 425 Americans if they watch this program regularly. Of the 425, 255 respond yes. Calculate the test statistic z for the population proportion. A) B) -2.7 C) 2.7 D) E) None of the above. 22) 23) State conclusion to significance test in terms of the null hypothesis 24) According to a recent poll the percentage of Americans who would vote for the incumbent president is 53%. If a random sample of 1 people in New York results in 45% who would vote for the incumbent, test the claim that the percentage of people in New York who would vote for the incumbent president is different from 53%. Use a.1 significance level. H: p =.53. Ha: p.53. =.1 Test statistic: z = P-Value =.19 State your conclusion about H. A) Do not reject H B) Do not reject Ha C) Reject H D) Draw a new sample. E) Reject Ha 24) 5

6 25) An article in a journal reports that 34% of American fathers take no responsibility for child care. A researcher claims that the figure is higher for fathers in the town of Cheraw. A random sample of 233 fathers from Cheraw yielded 96 who did not help with child care. Do the data provide sufficient evidence to conclude that in Littleton the proportion is higher than.34? Use a.5 significance level. H: p =.34 Ha: p >.34. =.5 Test statistic: z = P-Value =.12 State your conclusion in terms of the H. A) Reject H B) Do not reject Ha C) Do n ot reject H D) Accept H.34 E) Reject Ha 25) Provide an appropriate response. 26) The county health department has concerns about the chlorine level of.4% mg/ml at a local water park increasing to an unsafe level. The water department tests the hypothesis that the local water park's chlorine proportions have remained the same, and find a P-value of.5. Provide an appropriate conclusion A) There is a.5% chance of no change in the chlorine proportion. B) There is a 99.5% chance of no change in the chlorine proportion. C) We can say there is a.5% chance of seeing a change in the chlorine proportions in the results we observed from natural sampling variation. We conclude the chlorine proportion is higher. D) There's only a.5% chance of seeing no change in the chlorine proportion in the results we observed from natural sampling variation. We conclude the chlorine proportion is higher. E) We can say there is a.5% chance of seeing no change in the chlorine proportions in the results we observed from natural sampling variation. There is no evidence of a higher chlorine proportion, but we cannot conclude the chlorine proportion is the same. 26) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Perform a significance test for a population proportion using the P-value approach. 27) A manufacturer considers his production process to be out of control when defects exceed 3%. In a random sample of 8 items, the defect rate is 5% but the manager claims that this is only a sample fluctuation and production is not really out of control. At the.1 level of significance, do the data provide sufficient evidence that the percentage of defects exceeds 3%? 27) Perform a significance test for a population proportion using the critical value approach. 28) A supplier of 3.5" disks claims that no more than 1% of the disks are defective. In a random sample of 6 disks, it is found that 3% are defective, but the supplier claims that this is only a sample fluctuation. At the.1 level of significance, do the data provide sufficient evidence that the percentage of defects exceeds 1%? 28) 6

7 Answer Key Testname: 9_1&9_2 1) C 2) B 3) C 4) A 5) D 6) C 7) E 8) Alternate: The sample data either supports or does not support the claim: The sample evidence warrants rejection of the claim or does not warrant rejection of the claim. 9) A 1) A 11) E 12) A 13) D 14) B 15) B 16) B 17) D 18) D 19) D 2) A 21) E 22) B 23) C 24) A 25) A 26) D 27) Test statistic: z = 1.5. P-value =.1472 Fail to reject the null hypotheses. There is not sufficient evidence at the 1% significance level to conclude that the percentage of defects exceeds 3%. 28) H: p =.1 Ha: p >.1. =.1 Test statistic: z = P-value =. (to four decimal places) Reject the null hypothesis. There is sufficient evidence at the 1% significance level to conclude that the percentage of defects exceeds 1%. 7

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