Stats 110 Exam Study Guide
Stats 110 Exam Study Guide STA 210
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This 2 page Study Guide was uploaded by Lauren Mason on Friday September 16, 2016. The Study Guide belongs to STA 210 at University of Kentucky taught by Dustin Lueker in Fall 2016. Since its upload, it has received 49 views. For similar materials see Intro to Statistics in Statistics at University of Kentucky.
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Date Created: 09/16/16
Statistics Exam 1 Study Guide Statistic Sampling- Basic Language Population - Larger collection of subjects/items that you are interested in understanding something about. Sample - Subject/items that you are able to measure/interview. Chosen from population Sample Statistic – number that describes the sample. E.g. observed proportion in sample who answered “Yes” Population Parameter — number that describes the population. E.g. true proportion of all U.K. students who would answer “Yes” to “Do you support gay marriage?” Simple Random Sampling Simple Random Sample (SRS) of size n consists of n individuals chosen from the population in such a way that every set of n individuals had the same chance of being chosen. Conﬁdence Intervals The variability seen in a statistic from sample to sample is called “sampling variability.” conﬁdence interval formula … Variables p-hat : portion of the sample, a statistic sigma: standard deviation mu: mean z*: level of conﬁdence n: the entire population (x-bar): the sample mean s: sample standard deviation Empirical Rule Examples 1. Suppose a bell-shaped distribution has a mean µ = 12 and a standard deviation σ = 5.1. 68% of the observations will fall between what two values? The empirical rule states that about 68% of the observations will fall within one standard deviation of the mean so we add and subtract one standard deviation (5) from the mean (12). 12 ± 5(7, 17) 2. What % of the observations will fall between -3 and 27? Three standard deviations is 15. Three standard deviations below the mean is 12 - 15 = -3. Three standard deviations above the mean is 12 + 15 = 27. The empirical rule states that about 99.7% of the observations will fall within three standard deviations of the mean. Thus, about 99.7% of the observations will fall between -3 and 27. 3. What percent of the observations will fall below 17? I think this is most easily done by drawing the distributions and placing values on the various pieces. Given our nature of communication I’ll try to describe it using the graphic on page 135 of your workbook. 17 is one standard deviation away from the mean (12+5). Looking at the graphic, 34% of the observations will fall between 12 and 17 (the blue part to the right of the mean, µ). Half of the observations, 50% will fall below the mean of 12. So what percent of the observations will fall below 17? Well, 50% fall below 12 and 34% are between 12 and 17. Thus, 50% + 34% = 84% of the observations will fall below 17. Note: Using this logic we can also get that 100% - 84% = 16% of the observations would fall above 17.
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