Elements of Statistics Questionnaire

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Description

  1. Organize and describe data
    1. Define and distinguish between categorical (qualitative) and numerical (quantitative) data.
    2. Distinguish between data from an observational study and data from a designed experiment.
    3. Distinguish differences in data analysis and interpretation between observational data and data from designed experiments.
    4. Organize data in frequency tables and contingency tables.
    5. Construct appropriate graphical displays of qualitative and quantitative data for a given set of data.
    6. Describe the general shape of data, skewed left, skewed right, normal or symmetric.
    7. Calculate the measures of central tendency including mean and median.
    8. Calculate the measures of dispersion including range, standard deviation, variance, and interquartile range; explain the meaning of dispersion as it relates to a problem.
    9. Use a statistical package on a graphics calculator or a computer to enter data and analyze results.
    10. Measure the position of a data point by computing a percentile
  2. Find the theoretical probability of an event
    1. Use probability notation including the “or” condition and the “and” condition.
    2. Determine whether or not two events are mutually exclusive.
    3. Determine whether or not two events are independent.
    4. Calculate the probability of compound events.
    5. Calculate conditional probabilities; explain the meaning of conditional probabilities.
  3. Determine the probabilities of a random variable
    1. Distinguish between discrete and continuous random variables.
    2. Find and interpret the mean and the standard deviation of a probability distribution.
    3. Recognize Bernoulli populations.
    4. Use the normal distribution to solve percent problems for normally distributed populations.
    5. Use the normal distribution to solve probability problems for normally distributed random variables.
  4. Generate distributions for sample means
    1. Calculate the mean for a distribution of sample means.
    2. Calculate the standard deviation for a distribution of sample means.
    3. Assess normality of a set of data.
    4. Demonstrate the use of the Central Limit Theorem and explain its importance.
  5. Estimate the Mean and Proportion with both large and small samples
    1. Construct confidence intervals for a population mean and a difference of two population means and interpret them in context.
    2. Construct confidence intervals for a population proportion and a difference of two population proportions and interpret them in context.
  6. Use Hypothesis Tests with both large and small samples
    1. Perform hypothesis tests for a population mean and a difference of two population means and interpret results.
    2. Perform a hypothesis test for a population proportion and a difference of two population proportions and interpret results.
    3. Explain Type I error, Type II error, p-value, significance level and power of test in context.
    4. Perform Chi-squared tests.
  7. Make predictions with linear data
    1. Create a scatter plot and calculate a correlation coefficient for bivariate data.
    2. Construct a linear regression equation, interpret the results, and test significance of slope.
    3. Use a linear regression equation to make predictions about data.
    4. Calculate the coefficient of determination for a linear regression equation and interpret results.

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