# Ap Stats Chapter 9 Homework Solutions

194 The Practice of Statistics for AP*, 4/e Chapter 9 Section 9.1 Check Your Understanding, page 532: 1. (a) The parameter of interest is p=proportion of students at Jannie’s high school who get less than 8 hours of sleep at night. (b) The hypotheses are: 0H :0.85p=and H :0.85.ap≠2. (a) The parameter of interest is µ=mean amount of time that it takes to complete the census form. (b) The hypotheses are: 0:10H=and :10.aH>Check Your Understanding, page 539: 1. A Type I error in this setting would be to say that the new batteries last longer than 30 hours when, in fact, their average lifetime is 30 hours. 2. A Type II error in this setting would be to say that the new batteries do not last longer than 30 hours when, in fact, they do last longer than 30 hours. 3. The result of a Type I error would be that the company spends the extra money to produce these new batteries when they aren’t any better than the older, cheaper, type. The result of a Type II error would be that the company would not produce the new batteries, even though they were better. Arguments could be made for either of the errors being worse. For example, with a Type I error, the company would be wasting its money producing a new battery that wasn’t any better. With a Type II error the company would be losing out on potential profits by not producing the new, better, battery. Exercises, page 546: 9.1 0:0.12;Hp=:0.12aHp≠where pis the proportion of lefties in his school. 9.2 0:0.72;=:0.72a≠where pis the proportion of teens in Yvonne’s school who rarely or never fight with their friends. 9.3 0:115;H=:115aH>where is the average score on the SSHA for students at least 30 years of age at the teacher’s college. 9.4 0:12;H=:12aH<where is the average amount of hemoglobin in Jordanian children. 9.5 0:3;Hσ=:3aH>where is the standard deviation of the temperature in the cabin. 9.6 0:10;H=:10aH>where is the standard deviation of the distance jumped by the ski jumpers. 9.7 The null hypothesis always gives the value of the current situation. In the hypotheses given, the alternative gives the current situation. The alternative is supposed to give what we are looking for evidence for. The hypotheses should be 0:0.37;Hp=:0.37.aHp>9.8 We do not need to test hypotheses about the sample statistic. We know what that is exactly. What we need to test are hypotheses about the population parameter. Also, we are only interested in whether the situation has improved, so we need a one-sided alternative hypothesis. The hypotheses should be 0:0.37;Hp=:0.37.aHp>

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