Subsection 5.2 Summary of What You Have Learned in This Chapter
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The reasoning process of statistical inference
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The terms parameter to describe a numerical characteristic of a population or process and statistic to describe a numerical characteristic of a sample
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The symbol \(\pi\) to represent the probability of success for a process or the population proportion and \(\hat{p}\) to represent a sample proportion of successes
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The fundamental notion of sampling variability and how to simulate empirical sampling (null) distributions "by hand" (e.g., using cards) and using technology (e.g., with an applet)
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How to estimate and interpret a p-value
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How to use technology to calculate binomial probabilities, as well as exact p-values and confidence intervals (see Example 1.1)
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When and how to apply the Central Limit Theorem for a sample proportion to approximate the binomial distribution (for the values of \(n\) and \(\pi\)) with a normal distribution (and how to determine the mean and standard deviation of this distribution)
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How to use the technology to estimate p-values and confidence intervals using the normal approximation to the binomial distribution
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The formal structure of a test of significance about a process/population parameter (define the parameter, state null and alternative hypotheses, determine which probability model to use, calculate the p-value as specified by the alternative hypothesis under the assumption that the null hypothesis is true, decide to reject or fail to reject the null hypothesis for the stated level of significance, and state the conclusion in context)
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How to calculate and interpret \(z\)-scores
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What factors affect the size of the p-value
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Type I and Type II errors, Power: what they mean, how their probabilities are determined, and how they are affected by sample size and each other
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Either through Binomial or Normal calculations (see Example 1.2)
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The idea of a confidence interval as the set of plausible values of the parameter that could have reasonably led to the sample result that was observed
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How to interpret the "confidence level" of an interval procedure
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What factors affect the width, midpoint, and coverage rate of a confidence interval procedure
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The logic and trade-offs behind different confidence interval procedures
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The distinction between statistical and practical significance and how we assess each
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Biased sampling methods systematically over-estimate or under-estimate the parameter; the sampling distribution of a statistic from an unbiased sampling method will center at the value of the parameter of interest
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Random sampling eliminates sampling bias and allows us to use results from our sample to represent the population
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Ways to try to avoid non-sampling errors in a sample survey (see Investigation 1.15; Example 1.3)
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