invest_3ed.pdf

# Hypothesized probability s x alternative less greater

This preview shows pages 133–136. Sign up to view the full content.

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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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.
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).

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern