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Statistics - Common Mistakes and Tables

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    Study Guide Statistics – Common Mistakes and Tables 1. Common Mistakes Statistics can feel tricky because there are many ways to make small mistakes. But here’s the good news: most exam errors come from a short list of common oversights. If you learn to watch out for these, you can greatly improve your accuracy and confidence. 1. Mixing Up Standard Deviation and Variance A very common mistake is forgetting whether a formula needs standard deviation or variance . • Standard deviation: ( σ ) or (s) • Variance: ( σ 2 ) or (s 2 ) Quick rule: • To get variance , square the standard deviation • To get standard deviation , take the positive square root of the variance 2. Confusing One - Tailed and Two - Tailed Hypotheses Choosing the wrong type of test can throw off your entire hypothesis test. Use a one - tailed test when: • The hypothesis says one value is greater than another • Example: “Scores will be higher after training.” Use a two - tailed test when: • The hypothesis says values will be different , but doesn’t specify the direction • Example: “Scores will be different after training.” (could be higher or lower) Important reminder: Your null hypothesis and alternative hypothesis must cover all possibilities :

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    Study Guide • greater than (>) • less than (<) • equal to (=) 3. Forgetting to Split Alpha in a Two - Tailed Test If a test is two - tailed , you must split your significance level (( α )) into two equal parts. Example: • If ( α = 0.05), then each tail gets: That means you look up critical values using 0.025 , not 0.05 . Also remember: Alpha is always split when computing confidence intervals. 4. Misreading the Standard Normal (z) Table Not all z - tables show probabilities the same way, so it’s easy to read the wrong area. For example: • Some tables show the area at or below z • Some show the area between the mean and z In this case: Table 2 in Statistics Tables gives the area at or below z . So if you need the area to the right of z , use:

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    Study Guide 5. Using the Wrong Degrees of Freedom in a One - Sample t - Test When working with a one - sample t - test , your degrees of freedom are: Always subtract 1 from (n) before using the t - table. 6. Mixing Up Confidence Level and Confidence Interval These sound similar, but they mean different things. Confidence level = how confident you are (like 95%) It relates to the significance level and chance results. Confidence interval = the range of values where the true parameter may fall It goes from a low value to a high value based on the confidence level. 7. Confusing Interval Width and Margin of Error A confidence interval is always: The margin of error is the “plus or minus” part. The interval width is double the margin of error. Example: If a parameter is estimated as 46% ± 4% : • Margin of error = 4% • Interval width = 8% 8. Confusing Statistics with Parameters This mistake happens a lot because the symbols look similar.

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    Study Guide Parameters describe the population (usually unknown) • Use Greek letters like: o ( μ ) ( population mean) o ( σ ) ( population standard deviation) Statistics describe a sample (you can calculate them) • Examples: o ( x̄ ) (sample mean) o (s) (sample standard deviation) Key idea: You compute statistics to estimate parameters , but they are not interchangeable . 9. Confusing the Addition Rule and the Multiplication Rule These probability rules are used in different situations. Multiplication rule : use when all favorable outcomes must happen Example: You need event A and event B. Addition rule : use when at least one success must happen Example: You need event A or event B. 10. Forgetting That the Addition Rule Requires Mutually Exclusive Outcomes The addition rule works differently depending on whether outcomes can happen together. If outcomes are mutually exclusive , they cannot happen at the same time . Then you can just add probabilities. But if outcomes can occur together , you must subtract the overlap:

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    Study Guide 11. Forgetting to Average the Two Middle Values for an Even Median If your data set has an even number of values , the median is NOT one value — it’s the average of the two middle values. Steps: 1. Put the data in order 2. Find the two middle values 3. Take their mean This rule also matters sometimes when finding quartiles . 12. Placing Frequency Polygon Points in the Wrong Spot A frequency polygon should not use class interval endpoints. The points belong at the center (midpoint) of each class interval. Not at the edges — always at the middle . Quick Final Tip Most statistics mistakes happen because of small details like symbols, table values, tails, or formulas. If you slow down and double - check these common points, your work becomes much more reliable — and your exam scores can improve fast. 2. Statistics Tables Statistics tables can look super intimidating at first — lots of numbers, small print, and strange labels. But don’t worry: once you understand what each table is for and how to read it , they become one of the easiest tools to use on exams. This section includes four important tables: Table 1: Binomial Probabilities (for (n ≤ 20)) Table 2: Standard Normal (z) Probabilities

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    Study Guide Table 3: t Distribution Critical Values Table 4: Chi - Square (( χ 2 )) Critical Values

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    Study Guide

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