As you review the content in this book and work toward earning that 5 on your AP STATISTICS exam, here are five things that you MUST know:
1
Graders want to give you credit—help them! Make them understand what you are doing, why you are doing it, and how you are doing it. Don’t make the reader guess at what you are doing.
• Communication is just as important as statistical knowledge!
• Be sure you understand exactly what you are being asked to do or find or explain.
• Naked or bald answers will receive little or no credit! You must show where answers come from.
• On the other hand, don’t give more than one solution to the same problem—you will receive credit only for the weaker one.
2
Random sampling and random assignment are different ideas!
• Random sampling is use of chance in selecting a sample from a population.
– A simple random sample (SRS) is when every possible sample of a given size has the same chance of being selected.
– A stratified random sample is when the population is divided into homogeneous units called strata, and random samples are chosen from each strata.
– A cluster sample is when the population is divided into heterogeneous units called clusters, and a random sample of the clusters is chosen.
• Random assignment in experiments is when subjects are randomly assigned to treatments.
– This randomization evens out effects over which we have no control.
– Randomized block design refers to when the randomization occurs only within groups of similar experimental units called blocks.
3
Distributions describe variability! Understand the difference between:
• a population distribution (variability in an entire population),
• a sample distribution (variability in a particular sample), and
• a sampling distribution (variability between samples).
• The larger the sample size, the more the sample distribution looks like the population distribution.
• Central Limit Theorem: the larger the sample size, the more the sampling distribution (probability distribution of the sample means) looks like a normal distribution.
4
Check assumptions!
• Be sure the assumptions to be checked are stated correctly, but don’t just state them!
• Verifying assumptions and conditions means more than simply listing them with little check marks—you must show work or give some reason to confirm verification.
• If you refer to a graph, whether it is a histogram, boxplot, stemplot, scatterplot, residuals plot, normal probability plot, or some other kind of graph, you should roughly draw it. It is not enough to simply say, “I did a normal probability plot of the residuals on my calculator and it looked linear.”
5
Calculating the P-value is not the final step of a hypothesis test!
• There must be a decision to reject or fail to reject the null hypothesis.
• You must indicate how you interpret the P-value, that is, you need linkage. So, “Given that P = 0.007, I reject …” isn’t enough. You need something like, “Because P = 0.007 is less than 0.05, there is sufficient evidence to reject …”
• Finally, you need a conclusion in context of the problem.
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