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MATH 114 QUANTITATIVE REASONING FALL 2009 TEST 2 REVIEW SOLUTIONS 1. Suppose the prices of new laptops are normally distributed with a mean of $1300 and a standard deviation of $300. a) What percentage of new laptops cost less than $900? z 900 1300 400 1.333333333 300 300 the table says .0918, so 9.18% of laptops cost less than $900. b) What percentage cost between $1105 and $1730? Find each z score individually: z 1105 1300 195 0.65 the table says 0.2578 300 300 z 1730 1300 430 1.433333 the table says 0.9236 300 300 Since we want between these, we’ll subtract: 0.9236 – 0.2578 = 0.6658 so 66.58% of laptops are between $1105 and $1730 c) Kevin says his laptop cost more than 95% of all other laptops. How much did his laptop cost? Start with the table. Table says .9505 when z = 1.65. Put this into the equation and solve for x. 1.65 x 1300 300 1.65(300) x 1300 1.65(300) 1300 x So x = $1795. 2. I want to find out the mean length of all Radiohead songs, but I'm kind of lazy, so instead of actually finding the information for all Radiohead songs, I just look through 23 songs from a few different cd's I have. These 23 songs have a mean length of 3:28. It turns out, the actual mean length of all Radiohead songs is 3:52. For this scenario, identify the following: population _All Radiohead songs in the whole universe____ parameter value _3:52_____ sample __the 23 songs I sample___________________ statistic value __3:28_____ 3. For each of the following statistics, state the population which is being described and the variable being measured. “16% of students pay for some form of training or coaching when preparing for the SAT” Population – students preparing for the SAT Variable – whether or not they pay for coaching “Support for the new health care legislation is at 49%” Population – adult Americans Variable – whether or not they approve of health care legislation “Caffeine has been shown to reduce muscle soreness after exercising by 18%” Population – athletes Variable – level of muscle soreness 4. A pharmaceutical company believes its new supplement improves focus and learning ability and claims it will improve student performance. Using the five step process described in class, give a detailed outline of an experiment designed to test this claim. When appropriate, use specific terms such as: bias, confounding variable, control group, double-blind, placebo, population, sample, single-blind, and others. Step 1 Identify Population and Variable The supplement could probably be taken by anyone, but this study is focused on students. They’re probably not talking about my first grade daughter, so I think the population they have in mind is students ages 12 and up (or so). The thing they’re trying to measure is their focus – presumably they’d have to test them over some information they’re given in a potentially distracting setting. Peter Piper Pizza, for example. Step 2 Get a Sample Select a group of students. There will hopefully be variety among their ages and academic abilities. Step 3 Divide Sample Into Groups We want to try to test if this supplement improves focus, so we will put them all through some sort of information in – information out scenario and some of them will be given the supplement beforehand and some won’t. We could make the experiment single-blind by giving those who don’t receive the real supplement a sugar pill (placebo). We could make it double-blind by hiring other people to conduct the quizzing (say, Peter Piper employees) so that the observers would not know who had received the supplement. Step 4 Impose Treatment I’m envisioning something like a huge screen with images passing across it while lights are flashing and bells and whistles are going off – seriously Peter Piper Pizza style. The claim to be able to increase “focus,” so we have to design a scenario that will test that. Some will receive the supplement, some won’t. Maybe they’d do something more academic, but I like the Peter Piper approach. Step 5 Gather Results Record the participants scores on a quiz they take over the images they saw and compare between those took the supplement and those who didn’t. Some confounding variables could include: innate academic ability, mental state, amount of sleep participants had the night before, prior familiarity with academic material they were quizzed over, etc. 5. 1200 NAU students are surveyed and 441 said they like the band Radiohead. Create a 95% confidence interval for this statistic. Interpret your result. pˆ 441 0.3675 1200 s 0.3675(1 0.3675) .014 1200 So the confidence interval is from 0.37 – 2(0.014) to 0.37 + 2(0.014), or from 0.342 to .398. This means that I can be 95% confident that the true percent of NAU students who like Radiohead is between 34.2% and 39.8%.