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Statistics Final Exam Key Concepts

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  • Explanatory vs Response Variables

    Explanatory variable explains or predicts changes; response variable is the outcome measured.

  • Outliers vs Influential Points in Paired Data

    Outliers are extreme values; influential points strongly affect regression results. Both identified by residuals and leverage.

  • Choosing Correlation Coefficient

    Use Pearson's r for linear relationships; Spearman's rho for monotonic but non-linear; choose based on scatter plot pattern.

  • Linear Correlation Coefficient vs Critical Values

    Correlation coefficient measures strength/direction; critical values determine significance thresholds for hypothesis tests.

  • Determining Existence of Linear Correlation

    Check scatter plot pattern and test if correlation coefficient is significantly different from zero using hypothesis test.

  • Best Predicted y-value for Given x-value

    Use regression equation \(\hat{y} = b_0 + b_1 x\) to predict y from x.

  • Interpretation of \(R^2\)

    \(R^2\) indicates the proportion of variance in response variable explained by explanatory variable.

  • Difference Between Two Population Means Test

    Tests if two population means differ. Null: means equal; alternative: means differ. Uses t-distribution or z-distribution depending on data.

  • Reject and Fail to Reject Regions

    Regions defined by critical values where null hypothesis is rejected or not, based on test statistic and significance level.

  • Conclusion of Hypothesis Test

    Based on whether null is rejected or not, conclude if there is sufficient evidence to support alternative hypothesis.

  • Identifying Hypothesis Test Type from Prompt

    Determine if prompt fits Difference Between Means, Goodness of Fit, or ANOVA by data type and question focus.

  • Type I and Type II Errors

    Type I: Rejecting true null. Type II: Failing to reject false null. Errors depend on hypothesis and test design.

  • Hypothesis Test Distributions and Scores

    Use z-scores with Standard Normal, t-scores with Student-t, and chi-square scores with Chi-Square distribution depending on test.

  • Confidence Interval Width Factors

    Wider intervals mean less precision; affected by sample size, variability, and confidence level.

  • Interpretation of Confidence Interval

    Interval likely contains the true population parameter with specified confidence (e.g., 95%).

  • When to Use Standard Normal vs Student-t Distribution

    Use Standard Normal when population standard deviation known; Student-t when unknown and sample size small.

  • Standard Normal vs Normal Distribution

    Standard Normal is Normal with mean 0 and SD 1; Normal can have any mean and SD.

  • Central Limit Theorem Use

    Allows approximation of sampling distribution of sample mean to Normal for large samples regardless of population distribution.

  • Discrete vs Continuous Variables

    Discrete: countable values; Continuous: any value in interval. Different graph types represent each.

  • Requirements for Probability Distribution

    Probabilities sum to 1; each probability between 0 and 1; describes all possible outcomes.

  • Binomial vs Poisson Distributions

    Binomial: fixed trials, two outcomes; Poisson: counts events over interval, no fixed trials.

  • Frequency Distributions Purpose

    Summarize data by showing frequency of values or categories to understand data distribution.

  • Qualitative vs Quantitative Data

    Qualitative: categorical data; Quantitative: numerical data. Different graphs used for each.