3) A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz. 3)

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1 ch8aprac Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol (µ, p, ) for the indicated parameter. 1) An entomologist writes an article in a scientific journal which claims that fewer than 7 in ten 1) thousand male fireflies are unable to produce light due to a genetic mutation. Use the parameter p, the true proportion of fireflies unable to produce light. A) H0: p < B) H0: p = C) H0: p = D) H0: p > H1: p H1: p < H1: p > H1: p ) The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, µ, of 43 F, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect. A) H0: µ 43 B) H0: µ = 43 C) H0: µ 43 D) H0: µ 43 H1: µ > 43 H1: µ 43 H1: µ = 43 H1: µ < 43 2) 3) A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz. 3) A) H0: µ < 14 H1: µ 14 B) H0: µ = 14 H1: µ > 14 C) H0: µ > 14 H1: µ 14 D) H0: µ = 14 H1: µ < 14 4) The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, µ, of 41 F, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect. A) H0: µ = 41 B) H0: µ 41 C) H0: µ 41 D) H0: µ 41 H1: µ 41 H1: µ > 41 H1: µ = 41 H1: µ < 41 4) 5) A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the = 3.3 mg claimed by the manufacturer. A) H0: 3.3 mg B) H0: = 3.3 mg C) H0: 3.3 mg D) H0: 3.3 mg H1: < 3.3 mg H1: 3.3 mg H1: = 3.3 mg H1: > 3.3 mg 5) Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis. 6) = 0.05 for a two-tailed test. 6) A) ±1.96 B) ±2.575 C) ±1.645 D) ± ) = 0.09 for a right-tailed test. 7) A) 1.96 B) ±1.96 C) 1.34 D) ±1.34 8) = 0.05 for a left-tailed test. 8) A) ±1.645 B) C) D) ±1.96 9) = 0.1 for a two-tailed test. 9) A) ±2.052 B) ±2.33 C) ±1.645 D) ±

2 10) = 0.08; H1 is µ ) A) 1.41 B) 1.75 C) ±1.75 D) ±1.41 ^ Find the value of the test statistic z using z = p - p pq n. 11) A claim is made that the proportion of children who play sports is less than 0.5, and the sample statistics include n = 1671 subjects with 30% saying that they play a sport. A) B) C) D) ) The claim is that the proportion of drowning deaths of children attributable to beaches is more than 0.25, and the sample statistics include n = 681 drowning deaths of children with 30% of them attributable to beaches. A) B) 3.01 C) 2.85 D) ) The claim is that the proportion of accidental deaths of the elderly attributable to residential falls is more than 0.10, and the sample statistics include n = 800 deaths of the elderly with 15% of them attributable to residential falls. A) B) 3.96 C) 4.71 D) ) 12) 13) Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). 14) The test statistic in a right-tailed test is z = ) A) ; fail to reject the null hypothesis B) ; reject the null hypothesis C) ; reject the null hypothesis D) ; fail to reject the null hypothesis 15) The test statistic in a right-tailed test is z = ) A) ; reject the null hypothesis B) ; fail to reject the null hypothesis C) ; fail to reject the null hypothesis D) ; reject the null hypothesis 16) The test statistic in a left-tailed test is z = ) A) ; fail to reject the null hypothesis B) ; reject the null hypothesis C) ; fail to reject the null hypothesis D) ; reject the null hypothesis 17) The test statistic in a left-tailed test is z = ) A) ; fail to reject the null hypothesis B) fail to reject the null hypothesis C) ; reject the null hypothesis D) ; reject the null hypothesis 18) The test statistic in a two-tailed test is z = ) A) ; reject the null hypothesis B) ; reject the null hypothesis C) ; fail to reject the null hypothesis D) ; fail to reject the null hypothesis 19) The test statistic in a two-tailed test is z = ) A) ; fail to reject the null hypothesis B) ; fail to reject the null hypothesis C) ; fail to reject the null hypothesis D) ; reject the null hypothesis 20) With H1: p 0.612, the test statistic is z = ) A) ; fail to reject the null hypothesis B) ; fail to reject the null hypothesis C) ; reject the null hypothesis D) ; reject the null hypothesis 2

3 21) With H1: p 4/5, the test statistic is z = ) A) ; reject the null hypothesis B) ; reject the null hypothesis C) fail to reject the null hypothesis D) ; fail to reject the null hypothesis 22) With H1: p < 3/5, the test statistic is z = ) A) ; reject the null hypothesis B) 0.093; fail to reject the null hypothesis C) ; fail to reject the null hypothesis D) ; fail to reject the null hypothesis 23) With H1: p > 0.383, the test statistic is z = ) A) ; reject the null hypothesis B) ; fail to reject the null hypothesis C) ; fail to reject the null hypothesis D) ; reject the null hypothesis Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. 24) An entomologist writes an article in a scientific journal which claims that fewer than 12 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms. A) There is not sufficient evidence to support the claim that the true proportion is greater than 12 in B) There is sufficient evidence to support the claim that the true proportion is less than 12 in ten thousand. C) There is sufficient evidence to support the claim that the true proportion is greater than 12 in D) There is not sufficient evidence to support the claim that the true proportion is less than 12 in 25) Carter Motor Company claims that its new sedan, the Libra, will average better than 30 miles per gallon in the city. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms. A) There is not sufficient evidence to support the claim that the mean is greater than 30 miles per gallon. B) There is sufficient evidence to support the claim that the mean is greater than 30 miles per gallon. C) There is sufficient evidence to support the claim that the mean is less than 30 miles per gallon. D) There is not sufficient evidence to support the claim that the mean is less than 30 miles per gallon. 26) A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO, p, is less than 2 in every Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms. A) There is not sufficient evidence to support the claim that the true proportion is less than 2 in B) There is sufficient evidence to support the claim that the true proportion is greater than 2 in C) There is not sufficient evidence to support the claim that the true proportion is greater than 2 in D) There is sufficient evidence to support the claim that the true proportion is less than 2 in ten thousand. 24) 25) 26) 3

4 27) The owner of a football team claims that the average attendance at games is over 694, and he is therefore justified in moving the team to a city with a larger stadium. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms. A) There is sufficient evidence to support the claim that the mean attendance is less than 694. B) There is not sufficient evidence to support the claim that the mean attendance is less than 694. C) There is sufficient evidence to support the claim that the mean attendance is greater than than 694. D) There is not sufficient evidence to support the claim that the mean attendance is greater than ) A psychologist claims that more than 55 percent of the population suffers from professional problems due to extreme shyness. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms. A) There is not sufficient evidence to support the claim that the true proportion is less than 55 B) There is sufficient evidence to support the claim that the true proportion is less than 55 C) There is sufficient evidence to support the claim that the true proportion is greater than 55 D) There is not sufficient evidence to support the claim that the true proportion is greater than 55 29) The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, µ, of 49 F, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms. A) There is sufficient evidence to support the claim that the mean temperature is different from 49 F. B) There is not sufficient evidence to support the claim that the mean temperature is equal to 49 F. C) There is not sufficient evidence to support the claim that the mean temperature is different from 49 F. D) There is sufficient evidence to support the claim that the mean temperature is equal to 49 F. 30) A researcher claims that 62% of voters favor gun control. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms. A) There is sufficient evidence to warrant rejection of the claim that 62% of voters favor gun control. B) There is not sufficient evidence to warrant rejection of the claim that 62% of voters favor gun control. C) There is sufficient evidence to support the claim that more than 62% of voters favor gun control. D) There is not sufficient evidence to support the claim that 62% of voters favor gun control. 27) 28) 29) 30) 4

5 31) The principal of a middle school claims that test scores of the seventh-graders at his school vary less than the test scores of the seventh-graders at a neighboring school, which have variation described by = Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms. A) There is not sufficient evidence to support the claim that the standard deviation is greater than B) There is not sufficient evidence to support the claim that the standard deviation is less than C) There is sufficient evidence to support the claim that the standard deviation is less than D) There is sufficient evidence to support the claim that the standard deviation is greater than ) A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms. A) There is sufficient evidence to warrant rejection of the claim that the mean weight is less than 14 oz. B) There is not sufficient evidence to warrant rejection of the claim that the mean weight is at least 14 oz. C) There is sufficient evidence to warrant rejection of the claim that the mean weight is at least 14 oz. D) There is not sufficient evidence to warrant rejection of the claim that the mean weight is less than 14 oz. 33) A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the = 3.3 mg claimed by the manufacturer. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms. A) There is sufficient evidence to support the claim that the standard deviation is different from 3.3 mg. B) There is sufficient evidence to support the claim that the standard deviation is equal to 3.3 mg. C) There is not sufficient evidence to support the claim that the standard deviation is equal to 3.3 mg. D) There is not sufficient evidence to support the claim that the standard deviation is different from 3.3 mg. 31) 32) 33) Find the P-value for the indicated hypothesis test. 34) 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 130 of the school's students, 32% of them plan to go into general practice. Find the P-value for a test of the school's claim. A) B) C) D) ) In a sample of 88 children selected randomly from one town, it is found that 8 of them suffer from asthma. Find the P-value for a test of the claim that the proportion of all children in the town who suffer from asthma is equal to 11%. A) B) C) D) ) 35) 5

6 36) 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) B) C) D) ) A manufacturer claims that fewer than 6% of its fax machines are defective. In a random sample of 97 such fax machines, 5% are defective. Find the P-value for a test of the manufacturer's claim. A) B) C) D) ) 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 Littleton. A random sample of 225 fathers from Littleton, yielded 97 who did not help with child care. Find the P-value for a test of the researcher's claim. A) B) C) D) ) A nationwide study of American homeowners revealed that 65% have one or more lawn mowers. A lawn equipment manufacturer, located in Omaha, feels the estimate is too low for households in Omaha. Find the P-value for a test of the claim that the proportion with lawn mowers in Omaha is higher than 65%. Among 497 randomly selected homes in Omaha, 340 had one or more lawn mowers. A) B) C) D) ) An airline claims that the no-show rate for passengers booked on its flights is less than 6%. Of 380 randomly selected reservations, 18 were no-shows. Find the P-value for a test of the airline's claim. A) B) C) D) ) A random sample of 139 forty-year-old men contains 26% smokers. Find the P-value for a test of the claim that the percentage of forty-year-old men that smoke is 22%. A) B) C) D) ) Find the P-value for a test of the claim that less than 50% of the people following a particular diet will experience increased energy. Of 100 randomly selected subjects who followed the diet, 47 noticed an increase in their energy level. A) B) C) D) ) 37) 38) 39) 40) 41) 42) Answers: BBDAB ACBCC DBCDC BDCBD DACBB ADDAB CCDAA AABCC CC 6