Statistics Scope and Sequence

In this course we will cover the next topics:

• Unit 1. Introduction to Statistics.  The student will be introduced to the basic concepts and goals of statistics. The student will learn how data is collected from a sample and used to infer characteristics about the entire population.

1. Distinguish between a population and a sample.

2. Distinguish between a population parameter and a sample statistic.

3. Distinguish between descriptive statistics and inferential statistics.

4. Distinguish between qualitative data and quantitative data.

5. Distinguish between observational study and an experiment.

6. Classify data with respect to the four levels of measurement: nominal, ordinal, interval, and ratio.

7. Design a statistical study.

8. Design an experiment.

9. Create a sample using random sampling, simple random sampling, stratified sampling, cluster sampling, and systematic sampling; and identify a biased sample.

• Unit 2. Organizing Data. The student will learn different ways to organize and describe data sets. 

1. Construct a frequency distribution including limits, midpoints, relative frequencies, cumulative frequencies, and boundaries.

2. Construct frequency histograms, frequency polygons, relative frequency histograms, and ogives.

3. Graph and interpret quantitative data sets using stem-and-leaf plots and dot plots.

4. Graph and interpret qualitative data sets using pie charts and Pareto charts.

5. Graph and interpret paired data sets using scatter plots and time series charts.

• Unit 3. Central Tendency and Variation. Students will explore how to make data easier to understand by describing trends and measures of central tendency.

1. Find the mean, median, and mode of a population and of a sample.

2. Find a weighted mean of a data set and the mean of a frequency distribution.

3. Describe the shape of a distribution as symmetric, uniform, or skewed, and compare the mean and median for each.

• Unit 4. Variation. Students will explore how to make data easier to understand by describing measures of spread, and position.

1. Find the range of a data set and find the variance and standard deviation of a population and of a sample.

2. Use the Empirical Rule and the Chebychev’s Theorem to interpret standard deviation.

3. Approximate the sample standard deviation for a grouped data.

4. Use the coefficient of variation to compare variation in different data set

5. Find the first, second, and third quartiles of a data set, find the interquartile range of a data set, and represent a data set graphically using the box-and-whisker plot.

6. Interpret other fractiles such as percentiles and find percentiles for a specific data entry.

7. Find and interpret the standard score (z-score).

• Unit 5. Introduction to Probability. The student will be able to determine the probability of an event.

1. Identify the sample space of a probability experiment and how to identify simple events.

2. Use the Fundamental Counting Principle to find the number of ways two or more events can occur.

3. Distinguish among classical probability, empirical probability, and subjective probability.

4. Find the probability of the complement of an event and use the Fundamental Counting Principle to find probabilities.

• Unit 6. Conditional Probability. The student will explore probability rules for compound events.

1. Find the probability of an event given that another event has occurred.

2. Distinguish between independent and dependent events.

3. Use the Multiplication Rule to find the probability of two or more events occurring in sequence and to find conditional probabilities

4. Determine whether two events are mutually exclusive.

5. Use the Addition Rule to find the probability of two events

• Unit 7. Probability Distributions. The student will be able to create and use probability distributions. 

1. Distinguish between discrete random variables and continuous random variables.

2. Construct and graph a discrete probability distribution.

3. Determine whether a distribution is a probability distribution.

4. Find the mean, variance, and standard deviation of a discrete probability distribution

5. Find the expected value of a discrete probability distribution.

• Unit 8. Normal Distributions. The student will be able to recognize normal (bell-shaped) distributions and know how to use their properties in real-life applications

1. Interpret graphs of normal probability distributions.

2. Find areas under the standard normal curve.

3. Find probabilities for normally distributed variables using a table and using technology.

4. Find a z-score given the area under the normal curve.

5. Transform a z-score to an x-value 

6. Find a specific data value of a normal distribution given the probability.

• Unit 9. Sampling Distributions. The student will be able to find the mean and standard deviation of the sampling distribution of sample means. 

1. Find sampling distributions and verify their properties.

2. Interpret the Central Limit Theorem.

3. Apply the Central Limit Theorem to find the probability of a sample mean.

• Unit 10. Hypothesis Testing.  The student continues to study inferential statistics by testing a claim about a parameter.

1. 1. State a null hypothesis and an alternative hypothesis.

   2. Identify type I and type II errors.

   3. Know whether to use a one-tailed or a two-tailed statistical test.

   4. Interpret a decision based on the result of a statistical test.

   5. Find and interpret P-values.

   6. Find  P-values for a z-test for a mean μ  when σ  is known.

   7. Find critical values and rejection regions in the standard normal distribution.

   8. Use rejection regions for a z-test for a mean μ  when σ  is known.

   9. Use the z-test to test a population proportion p.

• Unit 11. Hypothesis Testing. The student continues to study inferential statistics by testing a claim about a parameter.

1. 1. State a null hypothesis and an alternative hypothesis.

   2. Identify type I and type II errors.

   3. Know whether to use a one-tailed or a two-tailed statistical test.

   4. Interpret a decision based on the result of a statistical test.

   5. Find and interpret P-values.

   6. Find  P-values for a z-test for a mean μ  when σ  is known.

   7. Find critical values and rejection regions in the standard normal distribution.

   8. Use rejection regions for a z-test for a mean μ  when σ  is known.

   9. Use the z-test to test a population proportion p.

• Unit 12. Hypothesis Testing with Two Samples. The student continues to study hypothesis testing by testing a hypothesis that compares two populations.

1. 1. Determine whether two samples are independent or dependent.

   2. Perform a two-sample z–test for the difference between two means and using independent samples with known standard deviations. 

   3. Perform a two-sample z–test for the difference between two population proportions.

• Unit 13. Correlation and Regression. The student will learn how to describe and test the significance of relationships between two variables when data are presented as ordered pairs.

1. Define linear correlation, independent and dependent variables, and the types of correlation.

2. Find a correlation coefficient.

3. Distinguish between correlation and causation.

4. Find the equation of a regression line.

5. Predict y-values using a regression equation.

6. Determine if a point is an outlier or an influential point.

7. Transform bivariate data to achieve linearity by using the exponential and power models.

8. Perform a linear regression.

9. Use the correlation coefficient to determine which linear model for the same set of data is the best fit.

• Unit 14. Chi-Square Test. The student will explore Hypothesis Testing for Categorical Data

1. Use the Chi-square distribution to test whether a frequency distribution fits an expected distribution.

2. Use a contingency table to find expected frequencies.

3. Use a Chi-square distribution to test whether two variables are independent.