# Elements of Statistics Questionnaire

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Description

- Organize and describe data
- Define and distinguish between categorical (qualitative) and numerical (quantitative) data.
- Distinguish between data from an observational study and data from a designed experiment.
- Distinguish differences in data analysis and interpretation between observational data and data from designed experiments.
- Organize data in frequency tables and contingency tables.
- Construct appropriate graphical displays of qualitative and quantitative data for a given set of data.
- Describe the general shape of data, skewed left, skewed right, normal or symmetric.
- Calculate the measures of central tendency including mean and median.
- Calculate the measures of dispersion including range, standard deviation, variance, and interquartile range; explain the meaning of dispersion as it relates to a problem.
- Use a statistical package on a graphics calculator or a computer to enter data and analyze results.
- Measure the position of a data point by computing a percentile

- Find the theoretical probability of an event
- Use probability notation including the “or” condition and the “and” condition.
- Determine whether or not two events are mutually exclusive.
- Determine whether or not two events are independent.
- Calculate the probability of compound events.
- Calculate conditional probabilities; explain the meaning of conditional probabilities.

- Determine the probabilities of a random variable
- Distinguish between discrete and continuous random variables.
- Find and interpret the mean and the standard deviation of a probability distribution.
- Recognize Bernoulli populations.
- Use the normal distribution to solve percent problems for normally distributed populations.
- Use the normal distribution to solve probability problems for normally distributed random variables.

- Generate distributions for sample means
- Calculate the mean for a distribution of sample means.
- Calculate the standard deviation for a distribution of sample means.
- Assess normality of a set of data.
- Demonstrate the use of the Central Limit Theorem and explain its importance.

- Estimate the Mean and Proportion with both large and small samples
- Construct confidence intervals for a population mean and a difference of two population means and interpret them in context.
- Construct confidence intervals for a population proportion and a difference of two population proportions and interpret them in context.

- Use Hypothesis Tests with both large and small samples
- Perform hypothesis tests for a population mean and a difference of two population means and interpret results.
- Perform a hypothesis test for a population proportion and a difference of two population proportions and interpret results.
- Explain Type I error, Type II error, p-value, significance level and power of test in context.
- Perform Chi-squared tests.

- Make predictions with linear data
- Create a scatter plot and calculate a correlation coefficient for bivariate data.
- Construct a linear regression equation, interpret the results, and test significance of slope.
- Use a linear regression equation to make predictions about data.
- Calculate the coefficient of determination for a linear regression equation and interpret results.

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