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Quiz 11.1A AP Statistics Name: At the bakery where you work, loaves of bread are supposed to weigh 1 pound. From experience, the weights of loaves produced at the bakery follow a Normal distribution with standard deviation = 0.13 pounds. You believe that new personnel are producing loaves that are heavier than 1 pound. As supervisor of Quality Control, you want to test your claim at the 5% significance level. You weigh 20 loaves and obtain a mean weight of 1.05 pounds. 1. Identify the population and parameter of interest. State your null and alternative hypotheses. 2. Identify the statistical procedure you should use. Then state and verify the conditions required for using this procedure. 3. Calculate the test statistic and the P-value. Illustrate using the graph provided. . 50 - 3. 0 3 .0 - . 50 4. State your conclusions clearly in complete sentences. Chapter 11 Quiz 11.1A Quiz 11.1B AP Statistics Name: Statistics can help decide the authorship of literary works. Sonnets by an Elizabethan poet are known to contain an average of = 6.9 new words (words not used in the poet’s other works). The distribution of new words in this poet’s sonnets is Normal with standard deviation = 2.7. Now a manuscript with five new sonnets has come to light, and scholars are debating whether it is the poet’s work. The new sonnets contain an average of x = 9.2 words not used in the poet’s known works. We expect poems by another author to contain more new words than found in the Elizabethan poet’s poems. 1. Identify the population and parameter of interest. State appropriate hypotheses in both words and symbols. 2. Identify the appropriate statistical procedure and verify conditions for its use. 3. Calculate the test statistic and the P-value. Illustrate using the graph provided. .50 -3.0 3 .0 -.50 4. State your conclusions clearly in complete sentences. Chapter 11 Quiz 11.1A Quiz 11.2A AP Statistics Name: Here are the Degree of Reading Power (DRP) scores for an SRS of 44 third-grade students from a suburban school district: 40 26 39 14 42 18 25 43 46 27 19 47 19 26 35 34 15 44 40 38 31 46 52 25 35 35 33 29 34 41 49 28 52 47 35 48 22 33 41 51 27 14 54 45 Suppose that the standard deviation of scores in this school district is known to be = 11. The researcher believes that the mean score of all third-graders in this district is higher than the national mean, which is 32. Carry out a significance test of the researcher’s belief at the 0.05 significance level. Chapter 11 Quiz 11.1A Quiz 11.2B AP Statistics Name: Here are measurements (in millimeters) of a critical dimension for a random sample of 16 auto engine crankshafts: 224.120 224.001 224.017 223.982 223.989 223.961 223.960 224.089 223.987 223.976 223.902 223.980 224.098 224.057 223.913 223.999 The data come from a production process that is known to have standard deviation = 0.060 mm. The process mean is supposed to be = 224 mm but can drift away from this target during production. Is there sufficient evidence to conclude that the mean dimension is not 224 mm? Give appropriate statistical evidence to support your conclusion. Chapter 11 Quiz 11.1A Quiz 11.3A AP Statistics Name: Read the brief newspaper article on using a depression pill to help smokers quit. Depression Pill Seems to Help Smokers Quit BOSTON — Taking an antidepression medicine appears to double smokers’ chances of kicking the habit, a study found. The Food and Drug Administration approved the marketing of this medicine, called Zyban or bupropion, to help smokers in May. The results of several studies with the drug, including one published in today’s issue of the New England Journal of Medicine, were made public then. The newly published study was conducted on 615 volunteers who wanted to give up smoking and were not outwardly depressed. They took either Zyban or dummy pills for 6 weeks. A year later, 23 percent of those getting Zyban were still off cigarettes, compared with 12 percent in the comparison group. 1. The results of this experiment were significant at the = 0.05 significance level. In your opinion, are the results practically significant? Justify your position. 2. To what population can the results of this study be generalized? Explain. 3. Can we conclude that taking Zyban causes people to quit smoking? Justify your answer. 4. In performing a test of significance, the researcher can choose between adopting a fixed significance level or calculating a P-value. Does it matter which approach is taken? If so, describe the circumstances when one should use each approach. Chapter 11 Quiz 11.1A Quiz 11.3B AP Statistics Name: Emissions of sulfur dioxide by industry set off chemical changes in the atmosphere that result in “acid rain.” The acidity of liquids is measured by pH on a scale of 0 to 14. Distilled water has pH 7.0, and lower pH values indicate acidity. “Normal” rain is somewhat acidic, so acid rain is sometimes defined as rainfall with a pH below 5.0. Suppose that pH measurements of rainfall on different days in a Canadian forest follow a Normal distribution with standard deviation = 0.5. A sample of n days finds that the mean pH is x = 4.8. Is this good evidence that the mean pH for all rainy days is less than 5.0? 1. Use the computer applet below to help you carry out a significance test at the 0.05 level. 2. The screen shots from the computer applet below are meant to illustrate a statistical lesson. Describe that lesson in a clearly written sentence or two. Chapter 11 Quiz 11.1A Quiz 11.4A AP Statistics Name: In a criminal trial, the defendant is held to be innocent until shown to be guilty beyond a reasonable doubt. If we consider hypotheses H0: defendant is innocent Ha: defendant is guilty we can reject H0 only if the evidence strongly favors Ha. 1. Is this goal better served by a test with = 0.20 or a test with = 0.01? Explain your answer. 2. Make a diagram that shows the truth about the defendant, and the possible verdicts and that identifies the two types of error. Which type of error is more serious? 3. Explain what is meant by the power of the test in this setting. Chapter 11 Quiz 11.1A Quiz 11.4B AP Statistics Name: Many suppliers use inspection procedures for quality control. For example, a contract between a manufacturer and a consumer for light bulbs may specify that the mean lifetime of the bulbs must be at least 1000 hours. As part of the quality assurance program, the manufacturer will institute an inspection program for each day's production of 10,000 units. An ordinary testing procedure is difficult since 1000 hours is over 41 days! Since the lifetime of a bulb decreases as the voltage applied increases, a common procedure is to perform an accelerated lifetime test in which the bulbs are lit using 400 volts (compared to the usual 110 volts). At such a voltage, a 1000-hour bulb will last (on average) only 3 hours. This is a well-known procedure, and both sides have agreed that the results from the accelerated test will be a valid indicator of lifetime of the bulb. The manufacturer proposes the following procedure: Hypotheses: H0: µaccelerated = 3 Ha: µaccelerated < 3 Sample 100 bulbs at random per day. Reject all lots whose P-value of the test-statistic is less than 0.05. In other words, the manufacturer will ship a day’s production unless the null hypothesis is rejected. 1. Describe a Type I and a Type II error in this setting. What are the consequences associated with each type of error? 2. Explain clearly two different things that could be done to increase the power of the proposed test procedure. Chapter 11 Quiz 11.1A