• Explain why probability is a core concept in statistics and the use of random sampling.

• Apply concepts in probability to the normal distribution, explain the relationship between z-scores and area under the curve, solving problems involving z-scores and percentiles.

• Explain the theory and purpose of a sampling distribution, calculate statistics for sampling distributions of the mean, and describe the implications of the central limit theorem.

• Explain the logic and process of null hypothesis significance testing, writing hypotheses in formal statistical terms and everyday language, and demonstrating knowledge of null hypothesis significance testing using the z-test.

• Compare and contrast Type I and Type II errors, explaining the probability with which each can be expected to occur

• Outline concerns associated with the reliance on p-values in data analysis, differentiating between statistical significance and importance.

• Buttress the use of hypothesis-testing methods with calculations and interpretation of effect size, confidence intervals, and power.

• Compare and contrast z- and t-distributions, and determine the appropriate test for various research situations.

• Develop and generate hypotheses for differences between means and conduct the corresponding tests.

• Calculate and interpret t-tests, effect sizes, and confidence intervals from raw data and summary statistics in both formal statistical terms and everyday language.

• Calculate effect sizes and required sample sizes to achieve desired statistical power, and interpret power curves for effect size and sample size.

• Generate and interpret confidence intervals for t-tests from raw data and summary statistics.

• Explain when to use chi-square analyses.

• Identify hypotheses appropriate for chi-square analyses.

• Explain the logic of chi-square analyses.

• Explain the assumptions of chi-square analyses.

• Conduct a chi-square goodness-of-fit test.

• Conduct a chi-square test of independence.

• Analyze effect size for chi-square analyses.

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