Hypothesized probability s x alternative less greater

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hypothesized probability ( S 0 ) x alternative (“less”, “greater”, or “two.sided”) x Optional: conf.level (s) Minitab Stat > Basic Statistics > 1 Proportion Use “normal approximation” under the Options button.
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Chance/Rossman, 2015 ISCAM III Chapter 1 Summary 133 Quick Reference to ISCAM R Workspace Functions in Chapter 1 (S. Lane-Getaz) Probability (or z-score) Desired Function Name(options)* Binomial Probability Right tail probability of Binomial random variable X, P(X > k | ࠵? ) iscambinomprob(k, n, pi, FALSE) Left tail probability of Binomial random variable X, P(X < k | ࠵? ) iscambinomprob(k, n, pi, TRUE) Exact Binomial Test and Confidence Interval Right/Left tail probability of Binomial random variable X, P(X > k | ࠵? ) iscambinomtest(k, n, pi, "greater") iscambinomtest(k, n, pi, "less") Two-tailed probability in Binomial distribution, P(X < k or X > k2 | ࠵? ) w/ method of small P-values iscambinomtest(k, n, pi, "two.sided") 95% (two-sided) Binomial confidence interval iscambinomtest(k, n, conf.level = c(90, 95)) Normal Probability Right/Left tail probability of Normal random variable X, P(X > x | ࠵? , ࠵? ) iscamnormprob(x, mu, sigma, "above", "x-axis-label") iscamnormprob(x, mu, sigma, "below", "x-axis-label") Two-tailed probabilities in Normal distribution, P(X < x1 or X > x2 | ࠵? , ࠵? ) iscamnormprob(x1, mu, sigma, "outside", "x-axis-label", x2) Probability between two values in Normal distribution, P(x1 < X < x2 | ࠵? , ࠵? ) iscamnormprob(x1, mu, sigma, "between", "x-axis-label", x2) Inverse Normal Probability z-score value with stated probability above/ below iscaminvnorm(probability, direction = "above") iscaminvnorm(probability, direction = "below") z-score value with stated probability outside iscaminvnorm(probability, direction = "outside") z-score value with stated probability between iscaminvnorm(probability, direction = "between") Normal (z-test) Approximation for One Proportion and Confidence Interval (CI) Right/Left tail probability of a proportion using Normal z-test, P( p ˆ > k/n | ࠵? ) iscamonepropztest(k, n, pi, "greater") iscamonepropztest(k, n, pi, "less") Two-tailed probability using Normal z-test, P( p ˆ < k/n or p ˆ > (1- k)/n | ࠵? ) iscamonepropztest(k, n, pi, "two.sided") 95% (two-sided) Normal confidence interval iscamonepropztest(k, n, conf.level = c(90, 95)) * In addition to numerical output these functions provide a graphical representation.
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Chance/Rossman, 2015 ISCAM III Chapter 1 Appendix 134 Chapter 1 Appendix - Stratified Random Sampling Another way to reduce variability without taking larger samples is to take even more care in our sampling. For example, a stratified sampling method splits the population into homogenous groups first, and then samples a preset proportion from each subgroup. In the Gettysburg Address example, if we suspect nouns tend to be longer than non-nouns but worry that with only 16% nouns in the population we could easily end up with a sample without nouns, we can force the sample to contain 3 nouns and 17 non-nouns. This method will again be unbiased and if we stratify on a useful variable, we should find even less random sampling variability. Below we see in this case that in stratified random samples of size 20, there is a little bit less variability of sample proportions (though not much here).
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