Hypothesis Testing Handout 1: Hypotheses, Tails, Errors Name___________________________________MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. A hypothesis test is to be performed. Determine the null and alternative hypotheses. 1) In the past, the mean running time for a certain type of flashlight battery has been 9.0 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 = 9.0 hours B) H : µ ≥ 9.0 hours 0 0 H : µ ≠ 9.0 hours H : µ = 9.0 hours a a C) H : µ ≠ 9.0 hours D) H : µ = 9.0 hours 0 0 H : µ = 9.0 hours H : µ > 9.0 hours a a 2) The maximum acceptable level of a certain toxic chemical in vegetables has been set at 0.6 parts per million (ppm). A consumer health group measured the level of the chemical in a random sample of tomatoes obtained from one producer to determine whether the mean level of the chemical in these tomatoes exceeds the recommended limit. A) H : µ = 0.6 ppm B) H : µ > 0.6 ppm 0 0 H : µ > 0.6 ppm H : µ = 0.6 ppm a a C) H : µ < 0.6 ppm D) H : µ = 0.6 ppm 0 0 H : µ > 0.6 ppm H : µ ≥ 0.6 ppm a a 3) A manufacturer claims that the mean amount of juice 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 B) H : µ < 16.1 ounces 0 0 H : µ < 16.1 ounces H : µ = 16.1 ounces a a C) H : µ > 16.1 ounces D) H : µ = 16.1 ounces 0 0 H : µ < 16.1 ounces H : µ ≤ 16.1 ounces a a Classify the hypothesis test as two-tailed, left-tailed, or right-tailed. 4) The recommended dietary allowance (RDA) of vitamin C for women is 75 milligrams per day. A hypothesis test is to be performed to decide whether adult women are, on average, getting less than the RDA of 75 milligrams per day. A) Two-tailed B) Left-tailed C) Right-tailed 5) The mean credit card debt among households in one state is $8400. A hypothesis test is to be performed to decide whether the mean credit card debt for households in the formerly affluent town of Rich -No-More differs from the mean credit card debt for the state. A) Two-tailed B) Left-tailed C) Right-tailed 4) 1) 2) 3) 5) 1 C) A Type I error would occur if. µ = 21. in 2006. C) A correct decision would occur if. in fact. B) A correct decision would occur if. in fact.1 ounces. but the results of the sampling lead to the conclusion that µ > 16.6 hours and the results of the sampling lead to that conclusion.6) A psychologist has designed a test to measure stress levels in adults. in fact. in fact. D) A correct decision would occur if. 8) 2 .6 hours. B) A Type I error would occur if. in fact. µ < 21. or a correct decision as specified. A) Two-tailed B) Left-tailed C) Right-tailed 6) For the given hypothesis test.6 hours. µ < 21. µ = 16. or if. in fact. in fact. 7) At one school.6 hours a where µ is the mean amount of time.1 ounces. D) A Type I error would occur if. and the results of the sampling do not lead to rejection of that fact. The hypotheses are: H : µ = 16. in fact. 8) A manufacturer claims that the mean amount of juice in its 16 ounce bottles is 16. a Type II error. but the results of the sampling lead to the conclusion that µ < 16. µ < 16. µ < 21. in fact. explain the meaning of a Type I error. The hypotheses are: H : µ = 21. or if. the principal performed a hypothesis test to determine whether the average amount of time spent watching television per week had decreased. The principal introduced a campaign to encourage the students to watch less television.6 hours and the results of the sampling lead to that conclusion. µ < 21. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this.6 hours and the results of the sampling do not lead to rejection of the null hypothesis that µ = 21.6 hours.1 ounces a where µ is the mean amount of juice in the manufacturer's 16 ounce bottles. but the results of the sampling fail to lead to that conclusion. µ = 16. µ = 21. One year later. the average amount of time that tenth-graders spent watching television 7) each week was 21.1 ounces. in fact.6 hours. µ = 21. in fact.1 ounces.1 ounces.1 ounces. that tenth -graders spend watching television each week Explain the meaning of a correct decision. and the results of the sampling lead to rejection of the null hypothesis. She has determined that nationwide the mean score on her test is 27. A hypothesis test is to be conducted to determine whether the mean score for trial lawyers exceeds the national mean score. in 2006. Explain the meaning of a Type I error. A) A correct decision would occur if. µ < 16.1 ounces.6 hours. and the results of the sampling do not lead to rejection of that fact. or if.1 ounces 0 H : µ < 16. in 2005.6 hours and the results of the sampling do not lead to rejection of the null hypothesis that µ = 21.6 hours 0 H : µ < 21.6 hours. A) A Type I error would occur if. but the results of the sampling do not lead to rejection of that fact. D) A Type I error would occur if. µ = 485. the mean math SAT score for students at one school was 485. a teacher performed a hypothesis test to determine whether the average math SAT score of students at the school had changed from the 2000 mean of 485. µ > $1200 and the results of the sampling do not lead to rejection of the null hypothesis that µ = $1200. in fact. in 2005. C) A correct decision would occur if. and the results of the sampling lead to rejection of the null hypothesis. The hypotheses were: H : µ = 485 0 H : µ ≠ 485 a where µ is the mean math SAT score. µ > $1200 and the results of the sampling lead to that conclusion. A) A Type I error would occur if. µ = $1200. in fact.9) A health insurer has determined that the "reasonable and customary" fee for a certain medical procedure is $1200. B) A correct decision would occur if. or if. or if. for students at the school Explain the meaning of a Type I error. 10) In 2000. in fact. in fact. A) A correct decision would occur if. The insurer wants to perform a hypothesis test to determine whether their suspicion is correct. µ ≠ 485. in fact. and the results of the sampling do not lead to rejection of that fact. D) A correct decision would occur if. µ > $1200 and the results of the sampling lead to that conclusion. in fact. and the results of the sampling lead to that conclusion. in 2005. but the results of the sampling do not lead to rejection of that fact 9) 10) 3 . µ = $1200. in fact. Five years later. The hypotheses are: H : µ = $1200 0 H : µ > $1200 a where µ is the mean amount charged by the clinic for this procedure. in fact. in fact. B) A Type I error would occur if. Explain the meaning of a correct decision. or if. but the results of the sampling fail to lead to that conclusion. µ = 485. in fact. They suspect that the mean fee charged by one particular clinic for this procedure is higher than $1200. µ ≠ 485. in fact. µ = $1200. but the results of the sampling lead to the conclusion that µ ≠ 485 C) A Type I error would occur if. and the results of the sampling do not lead to rejection of that fact. µ > $1200 and the results of the sampling do not lead to rejection of the null hypothesis that µ = $1200. 4 ppm. 12) In 2000. but the results of the sampling fail to lead to that conclusion. and the results of the sampling lead to rejection of the null hypothesis that µ = 0. µ ≠ 487. in fact. but the results of the sampling lead to the conclusion that µ > 0. in 2005. the defendant is innocent but the jury concludes that he is guilty. C) A Type II error would occur if.11) A man is on trial accused of murder in the first degree. the defendant is innocent and the jury fails to reject the null hypothesis that he is innocent. The hypotheses are H : µ = 0. in fact. Five years later.4 ppm. in fact. µ = 0. µ > 0. 0 H : The defendant is guilty. Explain the meaning of a Type I error. in fact. for students at the school Explain the meaning of a Type II error. µ = 487. The prosecutor presents evidence that he hopes will convince the jury to reject the hypothesis that the man is innocent. the defendant is guilty but the jury fails to conclude that he is guilty. µ > 0. in fact. B) A Type I error would occur if. A) A Type II error would occur if. a Explain the meaning of a Type II error. in fact. in fact. but the results of the sampling lead to the conclusion that µ ≠ 487 D) A Type II error would occur if. the defendant is guilty and the jury rejects the null hypothesis that he is innocent. in fact. µ = 0. B) A Type II error would occur if. the mean math SAT score for students at one school was 487. A) A Type II error would occur if. µ ≠ 487. A consumer health group measured the level of the chemical in a random sample of tomatoes obtained from one producer to determine whether the mean level of the chemical in these tomatoes exceeds the recommended limit. The hypotheses were: H : µ = 487 0 H : µ ≠ 487 a where µ is the mean math SAT score. 4 11) 12) 13) . in fact. D) A Type II error would occur if. in 2005.4 ppm a where µ is the mean level of the chemical in tomatoes from this producer. and the results of the sampling lead to that conclusion. A) A Type I error would occur if. 13) The maximum acceptable level of a certain toxic chemical in vegetables has been set at 0.4 parts per million (ppm). C) A Type I error would occur if. C) A Type II error would occur if. µ = 487. but the results of the sampling fail to lead to rejection of that fact.4 ppm.4 ppm D) A Type I error would occur if. This situation can be modeled as a hypothesis test with the following hypotheses: H : The defendant is innocent.4 ppm. in fact.4 ppm. a teacher performed a hypothesis test to determine whether the average math SAT score of students at the school had changed from the 2000 mean of 487. but the results of the sampling fail to lead to that conclusion. in fact. but the results of the sampling do not lead to rejection of that fact B) A Type II error would occur if. in fact.4 ppm 0 H : µ > 0. getting less than the RDA of 75 milligrams per day. in fact. but the results of the sampling lead to rejection of the null hypothesis that µ = 20. The hypotheses are: H : µ = 9. but the results of the sampling lead to the conclusion that µ > 20. µ = 20.9 hours a where µ is the mean running time of the new batteries Suppose that the results of the sampling lead to nonrejection of the null hypothesis. but the results of the sampling lead to the conclusion that µ < 75 mg D) A Type II error would occur if. Classify the conclusion of the hypothesis test as a Type I error. The hypotheses are H H 0 : µ = 75 mg 14) : µ < 75 mg a where µ is the mean vitamin C intake (per day) of all adult females. in fact. A) A Type II error would occur if. a Type II error. D) A Type I error would occur if. A) A Type I error would occur if. on average. or a correct decision. but the results of the sampling fail to lead to rejection of that fact. in fact. She has determined that nationwide the mean score on her test is 20. a Type II error. C) A Type I error would occur if. µ < 75 mg. The hypotheses are H : µ = 20 0 H : µ > 20 a where µ is the mean score for all trial lawyers. µ < 75 mg. or a correct decision.14) The recommended dietary allowance (RDA) of vitamin C for women is 75 milligrams per day. µ > 20. but the results of the sampling fail to lead to that conclusion. A) Type I error B) Type II error C) Correct decision 15) 16) 5 . Explain the meaning of a Type II error. in fact. if in fact the mean running time has increased.9 hours 0 H : µ > 9. Classify that conclusion as a Type I error. C) A Type II error would occur if. µ = 75 mg. µ = 20. 16) In the past. B) A Type II error would occur if. but the results of the sampling fail to lead to that conclusion. in fact. µ = 75 mg. in fact. in fact. and the results of the sampling do not lead to rejection of that fact. the mean running time for a certain type of flashlight battery has been 9. A hypothesis test is to be conducted to determine whether the mean score for trial lawyers exceeds the national mean score. B) A Type I error would occur if. A hypothesis test is to be performed to decide whether adult women are. 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 increased as a result. 15) A psychologist has designed a test to measure stress levels in adults. µ > 20. Explain the meaning of a Type I error. and the results of the sampling lead to rejection of the null hypothesis that µ = 75 mg.9 hours. in fact. 1 ounces a where µ is the mean amount of juice in the manufacturer's 16 ounce bottles. a Type II error. a Type II error.7 parts per million (ppm).7 ppm.1 hours. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this. if in fact the mean amount of juice.1 ounces. or a correct decision. or a correct decision. Suppose that the results of the sampling lead to rejection of the null hypothesis. Suppose that the results of the sampling lead to rejection of the null hypothesis.7 ppm 0 H : µ > 0. 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 increased as a result. A consumer health group measured the level of the chemical in a random sample of tomatoes obtained from one producer to determine whether the mean level of the chemical in these tomatoes exceeds the recommended limit.1 hours a where µ is the mean running time of the new batteries Suppose that the results of the sampling lead to rejection of the null hypothesis.1 hours 0 H : µ > 8.1 ounces 0 H : µ < 16. is less than 16. Classify that conclusion as a Type I error. A) Correct decision B) Type I error C) Type II error 17) 18) 19) 20) 6 .7 ppm a where µ is the mean level of the chemical in tomatoes from this producer. the mean running time for a certain type of flashlight battery has been 8. A) Type I error B) Correct decision C) Type II error 19) A health insurer has determined that the "reasonable and customary" fee for a certain medical procedure is $1200. Classify that conclusion as a Type I error. Suppose that the results of the sampling lead to nonrejection of the null hypothesis. if in fact the mean running time has not increased. The insurer wants to perform a hypothesis test to determine whether their suspicion is correct. if in fact the average fee charged by the clinic is $1200 .17) In the past. or a correct decision. if in fact the mean level of the chemical in these tomatoes is greater than 0. Classify that conclusion as a Type I error. The hypotheses are: H : µ = 16.1 ounces. a Type II error. A) Correct decision B) Type I error C) Type II error 20) The maximum acceptable level of a certain toxic chemical in vegetables has been set at 0. The hypotheses are: H : µ = $1200 0 H : µ > $1200 a where µ is the mean amount charged by the clinic for this procedure. The hypotheses are: H : µ = 8. Classify that conclusion as a Type I error. µ. They suspect that the average fee charged by one particular clinic for this procedure is higher than $1200. A) Correct decision B) Type I error C) Type II error 18) A manufacturer claims that the mean amount of juice in its 16 ounce bottles is 16. or a correct decision. The hypotheses are H : µ = 0. a Type II error. Answer Key Testname: HYPOTHESIS PRACTICE 1 1) A 2) A 3) A 4) B 5) A 6) C 7) C 8) B 9) C 10) B 11) C 12) D 13) C 14) D 15) C 16) B 17) B 18) B 19) B 20) C 7 .