SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

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1 Practice Exam 3 Summer 2007 Sec 7.2, 7.4, 8.2, 8.3, 8.5 Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) Under what conditions do you reject H0? Discuss both the traditional and the P-value approach. 2) Define P-values. Explain the two methods of interpreting P-values. 3) Discuss the rationale for hypothesis testing. Refer to the comparison of the assumption and the sample results. Solve the problem. 4) What do you conclude about the claim below? Do not use formal procedures or exact calculations. Use only the rare event rule and make a subjective estimate to determine whether the event is likely. Claim: A company claims that the proportion of defectives among a particular model of computers is 4%. In a shipment of 200 such computers, there are 10 defectives. 1

2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Express the null hypothesis H0 and the alternative hypothesis H1 in symbolic form. Use the correct symbol (µ, p, )for the indicated parameter. 5) 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. 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 ) Carter Motor Company claims that its new sedan, the Libra, will average better than 25 miles per gallon in the city. Use µ, the true average mileage of the Libra. A) H0: µ = 25 B) H0: µ > 25 C) H0: µ < 25 D) H0: µ = 25 H1: µ > 25 H1: µ 25 H1: µ 25 H1: µ < 25 7) 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 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. 8) = 0.09 for a right-tailed test. A) B) ±1.34 C) D) ±1.96 9) = 0.08; H1 is µ 3.24 A) ±1.75 B) 1.75 C) 1.41 D) ±1.41 2

3 Find the value of the test statistic z using z = ^ p - p. pq n 10) 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 = 615 drowning deaths of children with 30% of them attributable to beaches. A) 2.86 B) 2.71 C) D) Use the given information to find the P-value. 11) The test statistic in a right-tailed test is z = A) B) C) D) ) The test statistic in a left-tailed test is z = A) B) C) D) ) The test statistic in a two-tailed test is z = A) B) C) D) Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. 14) Carter Motor Company claims that its new sedan, the Libra, will average better than 21 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 sufficient evidence to support the claim that the mean is greater than 21 miles per gallon. B) There is not sufficient evidence to support the claim that the mean is greater than 21 miles per gallon. C) There is sufficient evidence to support the claim that the mean is less than 21 miles per gallon. D) There is not sufficient evidence to support the claim that the mean is less than 21 miles per gallon. 3

4 15) 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 not 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 different from 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 sufficient evidence to support the claim that the standard deviation is equal to 3.3 mg. Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test. 16) Carter Motor Company claims that its new sedan, the Libra, will average better than 26 miles per gallon in the city. Identify the type I error for the test. A) The error of rejecting the claim that the mean is at most 26 miles per gallon when it really is at most 26 miles per gallon. B) The error of rejecting the claim that the true proportion is more than 26 miles per gallon when it really is more than 26 miles per gallon. C) The error of failing to reject the claim that the mean is at most 26 miles per gallon when it is actually greater than 26 miles per gallon. 17) 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. Identify the type II error for the test. A) The error of failing to reject the claim that the standard deviation is 3.3 mg when it is actually different from 3.3 mg. B) The error of rejecting the claim that the standard deviation is 3.3 mg when it really is 3.3 mg. C) The error of rejecting the claim that the standard deviation is more than 3.3 mg when it really is more than 3.3 mg. 4

5 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. 18) A supplier of 3.5" disks claims that no more than 1% of the disks are defective. In a random sample of 600 disks, it is found that 3% are defective, but the supplier claims that this is only a sample fluctuation. At the 0.01 level of significance, test the supplier's claim that no more than 1% are defective. 19) In a sample of 167 children selected randomly from one town, it is found that 37 of them suffer from asthma. At the 0.05 significance level, test the claim that the proportion of all children in the town who suffer from asthma is 11%. 20) In a clinical study of an allergy drug, 108 of the 202 subjects reported experiencing significant relief from their symptoms. At the 0.01 significance level, test the claim that more than half of all those using the drug experience relief. 5

6 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the P-value for the indicated hypothesis test. 21) 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) Determine whether the given conditions justify testing a claim about a population mean µ. 22) The sample size is n = 18, is not known, and the original population is normally distributed. A) No B) Yes 23) The sample size is n = 44, = 13.4, and the original population is not normally distributed. A) Yes B) No SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. 24) The health of employees is monitored by periodically weighing them in. A sample of 54 employees has a mean weight of lb. Assuming that is known to be lb, use a 0.10 significance level to test the claim that the population mean of all such employees weights is less than 200 lb. 6

7 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the hypothesis test involves a sampling distribution of means that is a normal distribution, Student t distribution, or neither. 25) Claim: µ = 973. Sample data: n = 20, x = 958, s = 29. The sample data appear to come from a normally distributed population with = 28. A) Normal B) Student t C) Neither 26) Claim: µ = 105. Sample data: n = 18, x = 101, s = The sample data appear to come from a normally distributed population with unknown µ and. A) Student t B) Normal C) Neither 27) Claim: µ = 73. Sample data: n = 24, x = 104, s = The sample data appear to come from a population with a distribution that is very far from normal, and is unknown. A) Neither B) Student t C) Normal SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic, P-value, critical value(s), and state the final conclusion. 28) Test the claim that for the population of female college students, the mean weight is given by µ = 132 lb. Sample data are summarized as n = 20, x = 137 lb, and s = 14.2 lb. Use a significance level of = ) Test the claim that the mean age of the prison population in one city is less than 26 years. Sample data are summarized as n = 25, x = 24.4 years, and s = 9.2 years. Use a significance level of =

8 Test the given claim using the traditional method of hypothesis testing. Assume that the sample has been randomly selected from a population with a normal distribution. 30) A test of sobriety involves measuring the subject's motor skills. Twenty randomly selected sober subjects take the test and produce a mean score of 41.0 with a standard deviation of 3.7. At the 0.01 level of significance, test the claim that the true mean score for all sober subjects is equal to ) A test of sobriety involves measuring the subject's motor skills. Twenty randomly selected sober subjects take the test and produce a mean score of 41.0 with a standard deviation of 3.7. At the 0.01 level of significance, test the claim that the true mean score for all sober subjects is equal to ) A light-bulb manufacturer advertises that the average life for its light bulbs 900 hours. A random sample of 15 of its light bulbs resulted in the following lives in hours At the 10% significance level, do the data provide evidence that the mean life for the company's light bulbs differs from the advertised mean? 8