Principle of statistics pdf

Graphical representation of data. Measures of location - row data. Meausres of location - grouped data. Meausres of variation. Chebyshev and empirical rules. Coding data. Random experiment. Classical probability and counting rules. Conditional probability, Bayes and indep. Univariate random variables. Graphical displays Generate and interpret graphical displays of a given data set.

Random variables and sampling distributions Describe the distribution of random variables, sample means, and sample proportions. Probability calculations Calculate probabilities associated with statistics using properties of their sampling distributions. Relationship between variables Examine the relationship between two quantitative variables, two categorical variables, and a categorical and quantitative variable.

Residuals, or the difference between actual and predicted y-values, can be calculated and visualized on a scatter plot to help find a best fit model. Distributions have been addressed in other study topics and now this topic will go a bit deeper into this concept with sampling distributions. A sampling distribution differs from the other topics because it reflects the distribution of values from all possible samples taken from a set population.

The distribution can be described by its graphical shape on a histogram, median and standard deviation. Z-scores can also be calculated to determine the direction and number of standard deviations an observation is from the mean of the sample.

As noted at the beginning of the study guide, a z-score table will be provided in the exam. The central limit theorem is also part of this study topic. Part of probability theory, it essentially states that, if a population is very large, then its distribution can be considered normal.

It is an important component to the study of probability because it allows for the use of normal calculations on a sample from a large, non-normal population. Confidence intervals determine if the mean of a sample represents the mean of the population. Significance testing is a type of inference used to test evidence in the sample data for how well it describes the population.

The alternative hypothesis represents what is being tested and is only being tested as having an effect on the population or not, which is called the null hypothesis. Tests can be done in one direction one-tailed or for either direction two-tailed. To test an alternative hypothesis against the null, P-values measure the probability it is true, z-tests compare it to the known population data, and t-tests compare samples for significant differences. Type-1 or Type-2 errors can be made when testing an alternative hypothesis, so the probability of these errors can be understood with significance level and power tests.

Analysis of variance or ANOVA is a method for comparing two populations and should be reviewed for both one-way and two-way processes. The final segment of this study topic is non-parametric testing, such as the chi-square test for goodness of fit. Explanation: A z-score is a standardized value of observations in a sample that reflects the number of standard deviations away from the mean for each observation.

The z-score will be positive for observations higher than the sample mean and negative for observations below the mean. Using the multiplication rule, the combined probability of both events is 0. Explanation: The mean of the exam scores is 86 and the standard deviation of the scores is Thus, two standard deviations equal 26 and a student would need a 60 or below to take the exam again.

Correct Answer: D. Explanation: A confidence interval is an estimate of an unknown, such as the mean of the full population, with an indication of accuracy of the estimate.

Correct Answer: C. Both small OR smaller than the significance level. Explanation: A smaller P-value reflects stronger evidence against the null hypothesis. In addition, if the P-value is less than or equal to the significance level, the null hypothesis can be rejected. Normal distribution Probability histogram Uniform distribution Density curve. Explanation: Since a continuous random variable can take all values among some group of intervals, the probability any event can be described as the area below a density curve.

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