This document discusses various statistical concepts including measures of central tendency, probability, probability distributions, and inferential statistics techniques. It provides examples of how to identify the appropriate probability or distribution technique to use for a given problem, including the binomial, Poisson, and normal distributions. Key steps outlined include identifying the problem type, determining if it involves discrete or continuous data, and checking for conditions that indicate applying concepts like conditional probability or Bayes' theorem.
This document discusses various probability distributions including the binomial, Poisson, and normal distributions. It provides definitions and formulas for calculating probabilities for each distribution. For the binomial distribution, it covers the binomial probability formula and using the binomial table. For the Poisson distribution, it discusses the Poisson probability formula and Poisson table. It also addresses calculating the mean, variance, and standard deviation for the binomial and Poisson distributions. Finally, it introduces the normal distribution as the most important continuous probability distribution.
The document discusses simulation methods in econometrics and finance. It covers topics such as the Monte Carlo method, conducting simulation experiments by generating data and repeating experiments, random number generation, variance reduction techniques like antithetic variates and control variates, and examples of simulations in econometrics and finance including deriving critical values for Dickey-Fuller tests and pricing financial options. Bootstrapping methods are also discussed as an alternative to simulation that samples from real data rather than creating new data.
The document discusses several concepts related to sunk costs and rational decision making. It provides examples of how sunk costs can lead to irrational decisions through the sunk cost fallacy. Specifically, it discusses two hypothetical examples given by Richard Thaler where people decide to continue with plans or purchases even when it is no longer rational due to having already incurred some initial cost. The document also proposes models for incorporating sunk costs and transaction utility into rational decision making frameworks to better explain when the sunk cost fallacy occurs.
- The document describes Stanley Milgram's famous experiment on obedience to authority from 1963. In the experiment, participants were instructed to administer electric shocks to a learner for incorrect answers, though no actual shocks were given. - About 65% of participants administered what they believed were severe electric shocks, showing high obedience to authority. Each participant can be viewed as a Bernoulli trial with probability of 0.35 to refuse the shock. - The document then discusses using the binomial distribution to calculate probabilities of outcomes with a given number of trials and probability of success for each trial. It provides the formula and conditions for applying the binomial distribution.
1. This document discusses sample size calculation for research studies. 2. It explains that sample size determination is essential to allow for appropriate analysis, provide desired accuracy, and ensure validity of significance tests. 3. The key factors that affect sample size calculation are type of study, main outcome, variability between subjects, clinically important difference, type of measurement, and level of precision required.
Question 1 Independent random samples taken on two university campuses revealed the following information concerning the average amount of money spent on non-textbook purchases at the university’s bookstore during the fall semester. University A University B Sample Size 50 40 Average Purchase $260 $250 Population Standard Deviation(σ) $20 $23 We want to determine if, on the average, students at University A spent more on non-textbook purchases at the university’s bookstore than the students at University B. a. Compute the test statistic. b. Compute the p-value. c. What is your conclusion? Let α = .05. Question 2 In a residual plot against x that does not suggest we should challenge the assumptions of our regression model, we would expect to see a horizontal band of points centered near zero a widening band of points a band of points having a slope consistent with that of the regression equation a parabolic band of points Question 3 If we are testing for the equality of 3 population means, we should use the test statistic t test statistics z test statistic χ 2 test statistic F Question 4 The expected value of mean equals to the mean of the population from which the sample is drawn only if the sample size is 100 or greater for any sample size only if the sample size is 50 or greater only if the sample size is 30 or greater Question 5 A simple random sample of size n from a finite population of size N is to be selected. Each possible sample should have a probability of 1/n of being selected the same probability of being selected a probability of 1/N of being selected a probability of N/n of being selected Question 6 Consider the following results for two samples randomly taken from two normal populations with equal variances. Sample I Sample II Sample Size 28 35 Sample Mean 48 44 Population Standard Deviation 9 10 a. Develop a 95% confidence interval for the difference between the two population means. b. Is there conclusive evidence that one population has a larger mean? Explain. Question 7 As a general guideline, the research hypothesis should be stated as the null hypothesis hypothesis the researcher wants to disprove alternative hypothesis tentative assumption Question 8 As the degrees of freedom increase, the t distribution approaches the uniform distribution p distribution exponential distribution normal distribution Question 9 Two approaches to drawing a conclusion in a hypothesis test are p-value and critical value Type I and Type II one-tailed and two-tailed null and alternative Question 10 In hypothesis testing, the alternative hypothesis is the maximum probability of a Type I error All of the answers are correct the hypothesis tentatively assumed true in the hypothesis-testing procedure the hypothesis concluded to be true if the null hypothesis is rejected Question 11 For a two-tailed hypothesis test about μ, we can use any of the ...
Minimisation is an approach to allocating patients to treatment in clinical trials that forces a greater degree of balance than does randomisation. Here I explain why I dislike it.
This document appears to be a multiple choice quiz on quantitative techniques and statistics. It contains 36 multiple choice questions covering topics like correlation, normal distributions, probability, hypothesis testing, and regression. The questions range from calculating probabilities and percentages to identifying statistical concepts and relationships between variables based on data provided.
Statistics is a critical tool for robustness analysis, measurement system error analysis, test data analysis, probabilistic risk assessment, and many other fields in the engineering world. These basic applications are related to our basic engineering problems which help us to solve the problems and gives us the better solution and brings the efficiency to work with our real life engineering problems.