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| ap_statistics [2024/04/09 20:25] – mrdough | ap_statistics [2024/05/07 00:59] (current) – mrdough | ||
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| - | ====== | + | =======AP Statistics |
| - | + | Google doc Cheat sheet with stuff not on Formula Sheet [[https:// | |
| - | + | ---- | |
| - | **AP Statistics Study Guide** | + | |
| **From Simple Studies,** [[https:// | **From Simple Studies,** [[https:// | ||
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| * Mean of Y = 1/p | * Mean of Y = 1/p | ||
| - | * Standard deviation of Y = square root((1-p) / (p^2)) | + | * Standard deviation of Y = $\sqrt{((1-p) / (p^2))}$ |
| The **sampling distribution of the sample proportion** describes the distribution of values taken by the sample proportion in ALL POSSIBLE samples of the same size from the same population. | The **sampling distribution of the sample proportion** describes the distribution of values taken by the sample proportion in ALL POSSIBLE samples of the same size from the same population. | ||
| - | * SD = square root((p(1-p)) / n) *All conditions must be met* | + | * SD = $\sqrt{((p(1-p)) / n)} *All conditions must be met* |
| * Conditions: SRS, Independent, | * Conditions: SRS, Independent, | ||
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| * Individual observations must be independent | * Individual observations must be independent | ||
| - | * This allows us to calculate the standard deviation | + | * This allows us to calculate the standard deviation {{: |
| * When sampling without replacement, | * When sampling without replacement, | ||
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| When the standard deviation of a statistic is estimated from data, the result is called the **standard error** of the statistic | When the standard deviation of a statistic is estimated from data, the result is called the **standard error** of the statistic | ||
| - | * $\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$ | + | * {{: |
| These are the four-steps you MUST take when constructing a confidence interval: | These are the four-steps you MUST take when constructing a confidence interval: | ||
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| * As the degrees of freedom increase, the density curve approaches the standard normal distribution more closely | * As the degrees of freedom increase, the density curve approaches the standard normal distribution more closely | ||
| - | When the conditions are met, a C% confidence interval for the unknown mean is $x^-\pmt*(\frac{s_x}{\sqrt{n}})$ | + | When the conditions are met, a C% confidence interval for the unknown mean is {{: |
| * t* is the critical value for the t distribution with n - 1 degrees of freedom and C% of its area between -t* and t* | * t* is the critical value for the t distribution with n - 1 degrees of freedom and C% of its area between -t* and t* | ||
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| * Individual observations must be independent | * Individual observations must be independent | ||
| - | * This allows us to calculate the standard deviation using the formula | + | * This allows us to calculate the standard deviation using the formula {{: |
| * When sampling without replacement, | * When sampling without replacement, | ||
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| * Individual observations must be independent | * Individual observations must be independent | ||
| - | * This allows us to calculate the standard deviation | + | * This allows us to calculate the standard deviation {{: |
| * When sampling without replacement, | * When sampling without replacement, | ||
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| * Individual observations must be independent | * Individual observations must be independent | ||
| - | * This allows us to calculate the standard deviation | + | * This allows us to calculate the standard deviation {{: |
| * When sampling without replacement, | * When sampling without replacement, | ||
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| * The mean of the sampling distribution of p̂1 - p̂2 = p1 - p2 | * The mean of the sampling distribution of p̂1 - p̂2 = p1 - p2 | ||
| - | * The standard deviation of the sampling distribution of p̂1 - p̂2 = $\sqrt{ rac{p_1(1-p_1)}{n_1}+ rac{p_2(1+p_2)}{n_2}}$ | + | * The standard deviation of the sampling distribution of p̂1 - p̂2 = {{: |
| - | * The confidence interval is therefore | + | * The confidence interval is therefore {{: |
| * We can do this on our calculator through Stat > Tests > 2-PropZInt | * We can do this on our calculator through Stat > Tests > 2-PropZInt | ||
| * The 10% condition must be met for both samples | * The 10% condition must be met for both samples | ||
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| * The **mean** of the sampling distribution of x̅1 - x̅2 = μ1 - μ2 | * The **mean** of the sampling distribution of x̅1 - x̅2 = μ1 - μ2 | ||
| - | * The **standard deviation** of the sampling distribution of x̅1 - x̅2 = $\sqrt{ rac{\sigma^2_1}{n_1}+ rac{o^2_2}{m^2}}$ | + | * The **standard deviation** of the sampling distribution of x̅1 - x̅2 = {{: |
| - | * The confidence interval is therefore (𝑥̅1 − 𝑥̅2) ± $z*\sqrt{ rac{\sigma^2_1}{n_1}+ rac{o^2_2}{m^2}}$ | + | * The confidence interval is therefore (𝑥̅1 − 𝑥̅2) ± {{: |
| * We can use this through Stat > Tests > 2-SampTInt on the calculator | * We can use this through Stat > Tests > 2-SampTInt on the calculator | ||