Section 9.2 Hypothesis Tests for a Population Mean, Standard Deviation Known 409 calibration. (ii) The scale is not in calibration. (iii) The scale might be in calibration. a. Which of the three conclusions is best if H0 is rejected? (ii) b. Which of the three conclusions is best if H0 is not rejected? (iii) c. Assume that the scale is in calibration, but the conclusion is reached that the scale is not in calibration. Which type of error is this? Type I d. Assume that the scale is not in calibration. Is it possible to make a Type I error? Explain. No e. Assume that the scale is not in calibration. Is it possible to make a Type II error? Explain. Yes 30. IQ: Scores on a certain IQ test are known to have a mean of 100. A random sample of 60 students attend a series of coaching classes before taking the test. Let �� be the population mean IQ score that would occur if every student took the coaching classes. The classes are successful if �� > 100. A test is made of the hypotheses H0 : �� = 100 versus H1: �� > 100. Consider three possible conclusions: (i) The classes are successful. (ii) The classes are not successful. (iii) The classes might not be successful. a. Which of the three conclusions is best if H0 is rejected? (i) b. Which of the three conclusions is best if H0 is not rejected? (iii) c. Assume that the classes are successful but the conclusion is reached that the classes might not be successful. Which type of error is this? Type II d. Assume that the classes are not successful. Is it possible to make a Type I error? Explain. Yes e. Assume that the classes are not successful. Is it possible to make a Type II error? Explain. No Answers to Check Your Understanding Exercises for Section 9.1 1. H0: �� = 35, H1: �� > 35 2. H0: �� = 6.6, H1: �� ≠ 6.6 3. H0: �� = 25.5, H1: �� < 25.5 4. Correct decision 5. Type II error 6. Type I error SECTION 9.2 Hypothesis Tests for a Population Mean, Standard Deviation Known Objectives 1. Perform hypothesis tests with the critical value method 2. Perform hypothesis tests with the P-value method 3. Describe the relationship between hypothesis tests and confidence intervals 4. Describe the relationship between �� and the probability of error 5. Report the P-value or the test statistic value 6. Distinguish between statistical significance and practical significance Does coaching improve SAT scores? The College Board reported that the mean math SAT score in 2009 was 515, with a standard deviation of 116. Results of an earlier study (Preparing for the SAT — An Update, College Board Report 98–5) suggest that coached students should have a mean SAT score of approximately 530. Ateacher who runs an online coaching program thinks that students coached by his method have a higher mean score than this. We will see how to perform a hypothesis test to determine whether the teacher is right. There are two ways to perform hypothesis tests; both methods produce the same results. The first one we will discuss is called the critical value method. Then we will discuss the second method, known as the P-value method. Objective 1 Perform hypothesis tests with the critical value method The Critical Value Method In the SAT example, the teacher believes that the mean score for his students is greater than 530. Therefore, the null hypothesis says that the mean �� is equal to 530, and the alternate hypothesis says that �� is greater than 530. In symbols, H0 : �� = 530 H1: �� > 530 Now assume that the teacher draws a random sample of 100 students who are planning to take the SAT, and enrolls them in the online coaching program. After completing the program, their sample mean SAT score is ̄x = 562. This is higher than 530. Can he reject H0 and conclude that the mean SAT math score for his students is greater than 530?
navidi_monk_elementary_statistics_2e_ch7-9
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