Final Exam Study Guide PDF

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Final Exam Study GUIDE BUAD 310 1. Understand the meanings of and differences between categorical, ordinal and numerical variables. Categorical – categories such as gender, marital status, hometown aka qualitative data Ordinal – mixes numerical and categorical data. Numerical – aka quantitative data. Measurements such as height, weight or iq. -

Discrete Data – items that can be counted.

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Continuous data – cannot be counted. Could pump 8.40 gallons or 8.41 or 8.414863

2. Understand what a distribution of a variable is and how distributions are displayed.

The distribution of a variable is a description of the relative numbers of times each possible outcome will occur in a number of trials. The function describing the probability that a given value will occur is called the probability density function

Displayed on a curve 3. Understand and know how to use the words that describe distributions: Unimodal – having one mode, or one maximum Bimodal – two clear peaks skewed to the left - the mean is typically less than the median; the tail of the distribution is longer on the left hand side than on the right hand side; and. the median is closer to the third quartile than to the first quartile. skewed to the right - one in which the tail is on the right side. Right-skewed distributions are also called positive-skew distributions. That's because there is a long tail in the positive direction on the number line. The mean is also to the right of the peak

Symmetric Mode – most frequent value in a data set mean median minimum maximum range variance - Variance measures how far a data set is spread out. It is mathematically defined as the average of the squared differences from the mean. standard deviation - The standard deviation is the average amount of variability in your dataset. It tells you, on average, how far each value lies from the mean.

**Do I use STDEV P or STDEV s? P function is used when your data represents the entire population. The STDEV. S function is used when your data is a sample of the entire population. Quartile -

interquartile range percentile robust - Robust statistics, therefore, are any statistics that yield good performance when data is drawn from a wide range of probability distributions that are largely unaffected by outliers or small departures from model assumptions in a given dataset. In other words, a robust statistic is resistant to errors in the results. the five-number summary – the values seen below

box plot - ^ seen above histogram 4. Understand how correlation is used to show the linear relationship between two quantitative variables. Correlation is a term used to describe the relationship between two variables where the change in the value of one affects the value of the other.

5. Know how to interpret a scatterplot (form, direction, strength, positive and negative association).

6. Understand the possible values for correlation, r, and what these values mean. r is always a number between -1 and 1. r > 0 indicates a positive association. r < 0 indicates a negative association. Values of r near 0 indicate a very weak linear relationship

7. Understand the fundamental concepts of probability theory: random phenomena, sample space, events, probability of an event, equally likely events, the possible values for probability, empirical, classical and subjective approaches to assigning probabilities, law of large numbers, the rules of probability, the intersection of two events (A and B), the union of two events (A or B), the complement of an event, disjoint or mutually exclusive events, the general law of addition, the special law of addition, conditional probability, independent events, the general law of multiplication, and the special law of multiplication for independent events. 8. Know how to develop and interpret two-way tables (also called contingency tables)

A contingency table is a tabular representation of categorical data . A contingency table usually shows frequencies for particular combinations of values of two discrete random variable s X and Y. Each cell in the table represents a mutually exclusive combination of X-Y values.

9. Know how to use two-way tables to find joint, marginal and conditional probability distributions.

10. Understand random variables:

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the difference between discrete and continuous random variables

Continuous Variables would (literally) take forever to count. In fact, you would get to “forever” and never finish counting them. Discrete variables are countable in a finite amount of time.

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probability distribution functions and cumulative distribution functions for discrete and continuous random variables

The cumulative distribution function (c.d.f.) of a discrete random variable X is the function F(t) which tells you the probability that X is less than or equal to t. So if X has p.d.f. P(X = x), we have: F(t) = P(X £ t) = SP(X = x). In other words, for each value that X can be which is less than or equal to t, work out the probability that X is that value and add up all such results. the expected value, variance and standard deviation of a random variable.

https://towardsdatascience.com/expected-value-of-random-variables-explained-simplya0b02eebd9af 11. Know how to calculate the expected value and standard deviation of a discrete random variable.

12. Know the characteristics of the Uniform distribution. Suppose you want to know the probability of pulling a 2 of hearts from the modified deck. The probability of pulling a 2 of hearts is 1/40 or 2.5%. Each card is unique; therefore, the likelih https://www.investopedia.com/terms/u/uniform-distribution.asp#uniform-distribution-vsnormal-distribution 13. Understand Bernoulli experiments and how they lead to the binomial distribution. Bernoulli distribution is the discrete probability distribution of a random variable which takes the value 1 with probability p p and the value 0 with probability q = 1 − p {\displaystyle q=1-p}. Less formally, it can be thought of as a model for the set of possible outcomes of any single experiment that asks a yes–no question.

14. Recognize when it is appropriate to apply the binomial distribution and how to apply it.

Yes or no scenarios. Heads or tails 15. Know how to find the expected value and standard deviation of a linear function of a random variable (e.g., Y = aX + b).

???? 16. For a random variable with a continuous probability distribution, know what its probability density function (PDF) and cumulative distribution function (CDF) are and how the latter is used to find the probability the random variable is less than a given number, greater than a given number, or between two given numbers. Know how to use the CDF to find a given percentile. Be familiar with the uniform and normal density curves. Know how to convert a normal density curve with mean μ and standard deviation σ into a standard normal density with mean 0 and standard deviation 1.

17. Know how to use the appropriate Excel functions for the above distributions. 18. Know how to use the empirical rules for normal or near-normal distributions and for the standard normal distribution. 19. Know the key definitions in statistical inference: population, sample, survey, bias, simple random sample, estimator, estimate, parameter, statistic, unbiased estimator, population distribution, sampling distribution. 20. Know the mean and standard error of the sample mean, � !

21. Understand the nature of the sampling distribution of � if the population distribution is normal. ! 22. Understand the impact of sample size on the distribution of � regardless of the shape of the population distribution (the Central Limit Theorem).

23. Know the definition of population proportion π and the sample proportion p used to estimate it. 24. Understand the nature of the sampling distribution of p for n large and its mean and standard deviation. 25. Know how to construct a confidence interval for the population mean assuming you know the population standard deviation. 26. Understand the notions of confidence level and margin of error. 27. Understand how the width of a confidence interval is related to the confidence level, the standard error of the sample mean and the sample size. 28. Know how to construct a confidence interval for the population mean assuming you do not know the population standard deviation. 29. Understand the t distribution and the role of degrees of freedom and how it is used to construct a

confidence interval for the population mean assuming you do not know the population standard deviation. 30. Know how to use the appropriate Excel functions for the t distribution. 31. Know how to construct a confidence interval for the population proportion. ! 32. Know the definitions of standard error of the sample mean, �, and the standard error of the sample proportion, p. 33. Understand the general form of the confidence interval for a population mean and a population proportion, that is, what makes up the margin of error to be added and subtracted from the sample mean or sample proportion: a t multiplier times the standard error of the sample mean or a z multiplier times the standard error of the sample proportion. 34. Know how to calculate the sample size required to estimate a population proportion with a maximum error of ± E. 3 ! 35. Know what a hypothesis test is and how to conduct one. Know the definitions of and how to frame the null hypothesis and the alternative hypothesis. Know when to use one-tailed and twotailed alternatives. 36. Know what Type I and Type II errors are. Understand the trade-off between the two types of errors. 37. Understand the concept of a test statistic, how to calculate it given the sample data, and how to use it to decide whether or not to reject the null hypothesis. 38. Know the definition of the p-value and how to use it to decide whether or not to reject the null hypothesis. 39. Be able to do a t-test for a hypothesis test involving the sample mean. 40. Know what it means for the evidence against the null hypothesis provided by the data to be

statistically significant at level α. Know what it means for the p-value to be greater than or less than α. 41. Understand the equivalence among the notions of rejecting the null hypothesis at level α, finding a p-value less than α, and determining a t-statistic less than or greater than the value of t with α or α/2 in the appropriate tail or tails. 42. For a two-sided hypothesis test, understand the relationship between rejecting the null hypothesis at level α and whether or not the mean in the null hypothesis is in the (1 – α)100% confidence interval. 43. Know how to do a z-test for a null hypothesis involving the population proportion. 44. Know how to use the following Excel functions in connection with the above: AVERAGE, RAND(), STDEV.S, BINOM.DIST, NORM.DIST, NORM.S.DIST, NORM.INV, NORM.S.INV, T.DIST, T.INV, T.INV.2T, IF, AND, OR. 45. All the topics covered after the Midterm Exam....