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An extensive review of statistics concepts for an exam, including data classification (nominal, ordinal, interval, ratio), descriptive statistics (collecting, summarizing, and displaying data), inferential statistics (making claims or conclusions about a population based on sample results), sampling techniques (simple random, systematic, stratified, cluster, convenience), and probability distributions (normal, binomial, poisson). It covers key concepts, formulas, and excel functions.

Typology: Exams

2023/2024

1 / 7

Download Statistics Exam Review: Data Classification, Descriptive & Inferential Stats, Sampling and more Exams Computer Science in PDF only on Docsity! COB 191 Final Exam 2023 With Complete Solution Qualitative data - descriptive terms Quantitative data - described by numeric values Qualitative data classifications - nominal and ordinal Quantitative data classifications - interval and ratio Nominal - classifies data into distinct basic levels with no ranking implied Ordinal - classifies data into distinct basic levels where ranking is implied Interval - data can be meaningfully measured but has no true zero point Ratio - data can be meaningfully measured and has a true zero point Primary data - collected by you directly Secondary data - collected and published by someone else Discrete data - finite number range or countable number Examples of discrete data - money, number of children in a house, temperature Continuous data - infinite number, obtained by measuring, many decimal points Examples of continuous data - weight, height Descriptive statistics - collecting, summarizing, and displaying data; factual representation of sample information Inferential statistics - making claims or conclusions about the population based on sample results Simple random sampling - every member of the population has an equal chance of being chosen Systematic sampling - take every kth member as part of the sample, where k=N/n stratified random sampling - population is divided into strata and participants randomly selected from each stratum (subset of the population that shares a particular meaningful characteristic) cluster sampling - clusters are based on naturally occurring groups (like patients in a hospital) and participants are selected from those groups convenience sampling - used whenever participants are readily available measurement error - people provide incorrect data in survey coverage error - occurs when the sampling frame excludes some segments of the target population nonresponse bias - people who do not respond may be different from the people who do respond sampling error - sample mean-population mean ; varies from sample to sample relative frequency distribution - displays the proportion of observations of each class relative to the total number of observations cumulative relative frequency distribution - totals the proportion of observations that are less than or equal to the class which you are looking at formula for determining the number of classes in a frequency distribution - 2^k>/n Histogram gaps - discrete data no gaps in histogram - continuous data how many classes should be in a frequency distribution - between 4 and 20 width of bins formula - max-min ____________ k bin - maximum value that you want excel to count that fall within rules for classes for grouped data - 1. equal class sizes 2. mutually exclusive classes 3. include all data values 4. avoid empty classes if possible 5. avoid open ended classes if possible when would you use the median - when you have outliers in a data set excel formula for binomial distribution - =BINOM.DIST(x,n,p,cumulative) cumulative true - for fewer than successes cumulative false - for exactly x number of successes poisson distribution - useful for calculating the probability that a certain number of events will occur over a specific interval of time or space poisson distribution criteria - 1. mean (lambda) has to be the same for each interval 2. number of occurrences during one interval has to be independent 3. intervals cannot overlap poisson distribution excel formula - =POISSON.DIST(x, lambda, cumulative) when to use poisson distribution - number of customers per hour, number of accidents per month characteristics of normal probability distribution - 1. bell shaped and symmetrical around the mean 2. mean and median are the same values 3. total area is equal to 1 4. 50% on one side, 50% on the other side 5. left and right ends extend indefinitely how does the mean shape the normal distribution curve - shifts curve left or right how does the standard deviation shape the normal distribution curve - increases or decreases spread normal distribution excel function - =NORM.DIST(X, mean, st dev, cumulative) what is the probability of getting an exact value in continuous - 0 standard normal distribution - when x follows a normal distribution but you want to convert it into a z score normal excel function when given the area - =NORM.INV(probability, mean, st dev) normal excel function when given area and want standard deviation - =NORM.S.INV(probability) exponential probability distribution - commonly used to measure the time between events of interest exponential probability distribution excel function - =EXPON.DIST(x, lambda, cumulative) central limit theorem - the sample means of large-sized samples that will be normally distributed regardless of the population distribution standard error of the mean - population standard deviation divided by the square root of the sample size how many samples do you need for the central limit theorem - 30 what happens as sample size increases - standard error of the mean decreases what is the clt used for - checking the validity of claims made about a population parameter standard error of the proportion - take the square root of p(1-p)/n how to calculate sample proportion (p bar) - x/n confidence interval - an interval estimate around a sample mean that provides us with a range within which the true population mean is expected to lie how to calculate alpha - 1-confidence interval formula for confidence intervals - xbar+/-critical z score*standard error of the mean margin of error - critical z score*standard error of the mean characteristic of student t distribution - 1. bell shaped and symmetrical 2. area under the curve equals 1 3. flatter and wider than normal distribution 4. follows clt 5. critical t score is greater than critical z score when do you use student t distribution - when you aren't given population standard deviation critical t score excel function - =T.INV(alpha/2, degrees of freedom) how to calculate degrees of freedom - n-1 hypothesis - an assumption about a population parameter null hypothesis - represents the status quo </,=, or >/ alternative hypothesis - opposite of the null hypothesis >,=/, or < when do you use the two tail hypothesis test - when the alternative hypothesis is =/ (not equal to) when do you use the one tail hypothesis test - when the alternative hypothesis is < or > formula for z test statistic - (xbar-null hypothesis)/standard error of the mean p value - the probability of observing a sample mean at least as extreme as the one selected for the hypothesis test, assuming the null hypothesis is true p value >/ alpha - do not reject null hypothesis p value < alpha - reject null hypothesis how to calculate p value in excel - =NORM.S.DIST(z, cumulative) upper tail hypothesis test - null: mean </x alternative: mean >x lower tail hypothesis test - null: mean >/x alternative: mean <x formula for sampling distribution for differences in means - mean of xbar 1-mean of xbar 2 test statistic is greater than critical value - reject null test statistic is less than critical value - do not reject null