3.7STATISTICS IN SUMMARY
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• The purpose of sampling is to use a sample to gain information about a population. We often use a sample statistic to estimate the value of a population parameter.
• This chapter has one big idea: to describe how trustworthy a sample is, ask, “What would happen if we took a large number of samples from the same population?” If almost all samples would give a result close to the truth, we can trust our one sample even though we can’t be certain that it is close to the truth.
• In planning a sample survey, first aim for small bias by using random sampling and avoiding bad sampling methods such as voluntary response. Next, choose a large enough random sample to reduce the variability of the result. Using a large random sample guarantees that almost all samples will give accurate results.
• To say how accurate our conclusions about the population are, make a confidence statement. News reports often mention only the margin of error. Most often, this margin of error is for 95% confidence. That is, if we chose many samples, the truth about the population would be within the margin of error 95% of the time.
Page 52• We can roughly approximate the margin of error for 95% confidence based on a simple random sample of size n by the formula 1/√n. As this formula suggests, only the size of the sample, not the size of the population, matters. This is true as long as the population is much larger (at least 20 times larger) than the sample.
In Chapter 1, we introduced sample surveys as an important kind of observational study. In Chapter 2, we discussed both good and bad methods for taking a sample survey. Simple random sampling was introduced as a method that deliberately uses chance to produce unbiased data. This deliberate use of chance to produce data is one of the big ideas of statistics.
In this chapter, we looked more carefully at how sample information is used to gain information about the population from which it is selected. The big idea is to ask what would happen if we used our method for selecting a sample to take many samples from the same population. If almost all would give results that are close to the truth, then we have a basis for trusting our sample.
In practice, how easy is it to take a simple random sample? What problems do we encounter when we attempt to take samples in the real world? This is the topic of the next chapter.
CASE STUDY EVALUATED In the Case Study at the beginning of the chapter, 54% of those surveyed in 2015 felt that it is extremely important to vaccinate children. The Gallup Poll stated that childhood vaccinations were considered to be extremely important by a slight majority (54%) of American adults. Is 54% evidence that, in fact, the majority of American adults in 2015 felt that childhood vaccinations are extremely important? Use what you have learned in this chapter to answer this question. Your answer should be written so that someone who knows no statistics will understand your reasoning.
Online Resources
• The Statistical Applet Simple Random Sample can be used to select a simple random sample when the number of labels is 144 or fewer.