# Ch22.pdf - c hapter 22 Inferences About Means P...

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574Psychologists Jim Maas and Rebecca Robbins, in their bookSleep for Success!,say thatIn general, high school and college students are the most pathologicallysleep-deprived segment of the population. Their alertness during the day ison par with that of untreated narcoleptics and those with untreated sleep ap-nea. Not surprisingly, teens are also 71 percent more likely to drive drowsyand/or fall asleep at the wheel compared to other age groups. (Males underthe age of twenty-six are particularly at risk.)They report that adults require between 7 and 9 hours of sleep each night and claim thatcollege students require 9.25 hours of sleep to be fully alert. They note that “There is a19 percent memory deficit in sleep-deprived individuals” (p. 35).A student surveyed students at a small school in the northeast U.S. and asked, amongother things, how much they had slept the previous night. Here’s a histogram and the datafor 25 of the students selected at random from the survey.Inferences About Means22864246810Hours of SleepWe’re interested both in estimating the mean amount slept by college students and intesting whether it is less than the minimum recommended amount of 7 hours. These datawere collected in a suitably randomized survey so we can treat them as representative ofstudents at that college, and possibly as representative of college students in general.6767677786668885467858767chapter
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Chapter 12 / Exercise 5
Data Structures Using C++
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CHAPTER 22  Inferences About Means    575These data differ from data on proportions in one important way. Proportions aresummaries of individual responses, which had two possible values such as “yes” and “no,”“male” and “female,” or “1” and “0.” Quantitative data, though, report a quantitative valuefor each individual. When you have quantitative data, you should remember the threerules of data analysis and plot the data, as we have done here.Getting Started: The Central Limit Theorem (Again)You’ve learned how to create confidence intervals and test hypotheses about proportions.We always center confidence intervals at our best guess of the unknown parameter. Thenwe add and subtract a margin of error. For proportions, we writepn{ME.We found the margin of error as the product of the standard error,SE1pn2, and a criti-cal value,z*, from the Normal table. So we hadpn{z*SE1pn2.We knew we could usezbecause the Central Limit Theorem told us (back inChapter 17) that the sampling distribution model for proportions is Normal.Now we want to do exactly the same thing for means, and fortunately, the CentralLimit Theorem (still in Chapter 17) told us that a Normal model also works as the sam-pling distribution for means.The Central Limit TheoremWhen a random sample is drawn from any population with meanmand standarddeviations,its sample mean,y,has a sampling distribution with the samemeanmbut whosestandard deviationiss1naand we writes1y2=SD1y2=s1nb.

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Term
Fall
Professor
Morris
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Chapter 12 / Exercise 5
Data Structures Using C++
Malik
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