Unit 9 Statistics

Lesson 1

Learning Focus

Understand features of a normal distribution.

Identify the effect of changing the mean or standard deviation in a normal distribution.

Lesson Summary

In this lesson, we learned about features of a normal distribution. We learned a normal distribution is defined by the mean, which is the center of the distribution and the standard deviation, which determines the spread of the distribution. Normal distributions are represented with the $68 – 95 – 99.7 %$ rules, which describe the percent of the distribution within one standard deviation, two standard deviations, and three standard deviations, respectively, from the mean.

Lesson 2

Learning Focus

Interpret standardized test scores that are distributed normally.

Lesson Summary

In this lesson, we sketched a normal distribution and used it to estimate population percentages. We found a process that helps to visualize the region included so that the $68 – 95 – 99.7 %$ rule can be used.

Lesson 3

Learning Focus

Understand a scale used to compare normal distributions.

Sketch distribution curves and use tables to find population percentages.

Lesson Summary

In this lesson, we learned about the standard normal distribution and the $z$ -score, which is a method for putting all normal distributions on the same scale so they can be compared. Once a $z$ -score is computed for a given value, a $z$ -score table is used to find the population percentage to the left of the value.

Lesson 4

Learning Focus

Compare normal distributions.

Lesson Summary

In this lesson, we used features of a normal distribution—including the symmetry, the mean, and the standard deviation—to determine how unusual a given event may be.

Lesson 5

Learning Focus

Understand methods for taking samples from a population.

Lesson Summary

In this lesson, we learned about methods for obtaining samples from a population so that a parameter of interest can be studied. We learned that random sampling methods are preferable to other methods because they are more likely to represent the entire population.

Lesson 6

Learning Focus

Describe the difference between a survey, an experiment, and an observational study.

Design an investigation for a parameter of interest using appropriate study and sampling methods.

Lesson Summary

In this lesson, we learned about three methods for investigating a research question. The methods are surveys, observational studies, and experiments. For the results of any of the investigations to be valid, researchers must use a random sampling method to select participants from the population.

Lesson 7

Learning Focus

Represent the number of possible outcomes for a situation using diagrams, charts and formulas.

Compute probabilities using strategies.

Lesson Summary

In this lesson, we represented situations with tree diagrams, and other visual methods to count the possible outcomes for a situation. We applied the Fundamental Counting Principle and learned about two different ways to count possible outcomes, permutations and combinations. Permutations are used when the order of the items selected matters. Combinations are used when the order of the items in the group does not matter.

Lesson 8

Learning Focus

Determine if two events are independent.

Find the probabilities of independent events.

Lesson Summary

In this lesson, we used two methods to show that events are independent. The first method relies on conditional probability, and the second method is the Multiplication Rule. We also used the Multiplication Rule to find the probability of the intersection of two independent events.

Lesson 9

Learning Focus

Determine if events are independent.

Use representations to find probabilities.

Lesson Summary

In this lesson, we combined the rules and relationships we have learned for probability to determine if events are independent and to find conditions that make events independent. We learned that when conditional probabilities such as $P (A | B)$ are available, it is efficient to see if the conditional probability is equal to $P (A)$ to determine if $A$ and $B$ are independent. If probabilities of unions and intersections are available, it may be more efficient to use the Multiplication Rule to test for independence.

Lesson 10

Learning Focus

Perform a simulation to determine if an event can occur.

Lesson Summary

In this lesson, we used simulation to model the outcome of a random event. Using many trials, we created a distribution and used it to predict the likelihood of an event.

Lesson 11

Learning Focus

Use random sampling methods and find means and proportions for random samples.

Lesson Summary

In this lesson, we sampled a population and used the mean and proportion of the population to estimate the actual mean and proportion of the sample, which are called population parameters. We learned about the Central Limit Theorem, which says that if the sample is large enough, the sample means and proportions will be normally distributed.

Lesson 12

Learning Focus

Find an interval that is likely to contain the population proportion from a sample.

Lesson Summary

In the lesson, we learned to find an interval from a sample proportion that is likely to contain the population proportion using a margin of error. To use the formula, we found the sample size must be large enough to satisfy the conditions of the Central Limit Theorem.

Lesson 13

Learning Focus

Use simulation to find a plausible interval for the mean of a population from a sample.

Lesson Summary

In this lesson, we found a margin of error for a sample mean, which creates a plausible interval for the population mean. We learned that to use the margin of error formula, we must have a sample size of at least 30. We also learned how to find the likelihood that a sample comes from a population with a given mean and standard deviation.

Lesson 14

Learning Focus

Determine if the results of an experiment could have occurred by chance.

Lesson Summary

In this lesson, we used a simulation to determine if the results of an experiment could have occurred by chance. We found that simulation is useful not only for sampling but also for evaluating experimental results.

Lesson 15

Learning Focus

Use statistical reasoning to evaluate claims in the media.

Lesson Summary

In this lesson, we evaluated statistical claims from media sources. We found that we need to pay attention to sample size and methods and compare the plausible intervals when drawing conclusions.