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Trigonometry and Statistics Unit 5
Trigonometry and Statistics Unit 5

Powerpoint
Powerpoint

November 12 -- Estimation of a Mean, large sample size
November 12 -- Estimation of a Mean, large sample size

... noted in items 4 and 5, other levels may be more appropriate. 4. Comparison with other research. If a particular confidence level has been used in a research report or journal article, and you wish to compare your results with this research, use the same level as was used in the other research repor ...
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[17] Ross M, Mahfouz R, Onciu M, et al. Gene expression profiling of
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... 3. People with type O-negative blood are universal donors. That is, any patient can receive a transfusion of O-negative blood. Only 7.2% of the American population have O-negative blood. If 10 people appear at random to give blood, what is the probability that at least 1 of them is a universal dono ...
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... 12. In a hybrid corn research project, 200 seed were planted, and 170 of them germinated. find the empirical probability that any particular seed of this type will germinate. 13. In a certain state, 38,550 boys and 35,770 girls were born in 1996. Find the empirical probability that one of those bir ...
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... of multilocus NCPA was to eliminate the false-positives from single-locus inferences through another series of statistical tests that cross-validate the initial set of single-locus inferences. The false-positive rates for single locus NCPA are therefore irrelevant to multilocus NCPA. These additiona ...
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... (SSHA) is a psychological test that measures the motivation, attitude toward school, and study habits of students. Scores range from 0 to 200. The mean score for US college students is about 115, and the standard deviation is about 30. A teacher who suspects that older students have better attitudes ...
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Week 4, 9/10/12 - 9/14/12, Notes: Random Variables, PMFs

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... 7. Psychologists have determined that the time it takes a rat to find its way through a maze is exponentially distributed. Let x be the time in seconds, and for a particular maze the probability density function is f ( x)  0.025e0.025 x seconds, x  0 . (Note: an exponential pdf) a. Find the proba ...
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...  If the sample size is small (< 30), you should use a box-and-whisker plot or a normal probability plot to assess whether the assumption of normality is valid.  If the sample size is large, the central limit theorem applies and the sampling distribution of the mean will be normal. Statistics for M ...
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Statistics



Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In applying statistics to, e.g., a scientific, industrial, or societal problem, it is conventional to begin with a statistical population or a statistical model process to be studied. Populations can be diverse topics such as ""all persons living in a country"" or ""every atom composing a crystal"". Statistics deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments.When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can safely extend from the sample to the population as a whole. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation.Two main statistical methodologies are used in data analysis: descriptive statistics, which summarizes data from a sample using indexes such as the mean or standard deviation, and inferential statistics, which draws conclusions from data that are subject to random variation (e.g., observational errors, sampling variation). Descriptive statistics are most often concerned with two sets of properties of a distribution (sample or population): central tendency (or location) seeks to characterize the distribution's central or typical value, while dispersion (or variability) characterizes the extent to which members of the distribution depart from its center and each other. Inferences on mathematical statistics are made under the framework of probability theory, which deals with the analysis of random phenomena.A standard statistical procedure involves the test of the relationship between two statistical data sets, or a data set and a synthetic data drawn from idealized model. An hypothesis is proposed for the statistical relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis of no relationship between two data sets. Rejecting or disproving the null hypothesis is done using statistical tests that quantify the sense in which the null can be proven false, given the data that are used in the test. Working from a null hypothesis, two basic forms of error are recognized: Type I errors (null hypothesis is falsely rejected giving a ""false positive"") and Type II errors (null hypothesis fails to be rejected and an actual difference between populations is missed giving a ""false negative""). Multiple problems have come to be associated with this framework: ranging from obtaining a sufficient sample size to specifying an adequate null hypothesis.Measurement processes that generate statistical data are also subject to error. Many of these errors are classified as random (noise) or systematic (bias), but other important types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also be important. The presence of missing data and/or censoring may result in biased estimates and specific techniques have been developed to address these problems.Statistics can be said to have begun in ancient civilization, going back at least to the 5th century BC, but it was not until the 18th century that it started to draw more heavily from calculus and probability theory. Statistics continues to be an area of active research, for example on the problem of how to analyze Big data.
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