AP Statistics formulas and hypothesis test selection as cloze cards, with each variable defined.
33 cards · cloze cards · AI-written, checked twice. Edit anything.
- The z-score for a value x in a normal distribution with mean μ and standard deviation σ is ____
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z = (x - μ) / σ- A z-test for a population mean is used when the population standard deviation σ is ____ or the sample size n is very large
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known- In a normal distribution, approximately ____ of data falls within one standard deviation of the mean
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68%- For a 95% confidence level, the critical z-value z* is ____
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1.96- The test statistic for a one-sample t-test is ____, where x-bar is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size
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t = (x-bar - μ) / (s / sqrt(n))- The degrees of freedom for a one-sample t-test is ____, where n is the sample size
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n - 1- To use a one-sample t-test, the population must be ____ or the sample size must be large enough (n ≥ 30) by the Central Limit Theorem
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approximately normal- A confidence interval for a population mean when σ is unknown is ____, where t* is the critical t-value, x-bar is the sample mean, s is the sample standard deviation, and n is the sample size
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x-bar ± t* * (s / sqrt(n))- We use the ____ instead of the normal distribution when the population standard deviation σ is unknown and must be estimated by the sample standard deviation s
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t-distribution- The test statistic for a two-sample t-test for independent samples is ____, where s1 and s2 are the sample standard deviations and n1 and n2 are the sample sizes
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t = (x-bar1 - x-bar2) / sqrt((s1^2 / n1) + (s2^2 / n2))- For a two-sample t-test with unequal variances (Welch's test), the degrees of freedom is ____ and is typically between the smaller of (n1-1) and (n2-1) and the sum (n1+n2-2)
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calculated from a complex formula- For paired samples, the test statistic is ____, where d-bar is the mean difference, sd is the standard deviation of differences, and n is the number of pairs
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t = d-bar / (sd / sqrt(n))- A paired t-test is used when ____ or measurements are matched by design
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the same subjects are measured twice- A confidence interval for the difference between two independent population means is ____, where t* is the critical t-value
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(x-bar1 - x-bar2) ± t* * sqrt((s1^2 / n1) + (s2^2 / n2))- The test statistic for a one-sample z-test for a population proportion is ____, where p-hat is the sample proportion, p0 is the hypothesized population proportion, and n is the sample size
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z = (p-hat - p0) / sqrt((p0(1 - p0)) / n)
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