# Final Exam Study guide

## Instructions

The Final Exam will take place from 9:50 AM until 11:50 AM on Tuesday May 12. This will be open-book and open-note, and you are expected to use StatCrunch to solve problems on the exam. The Final Exam will be a total of $$21$$ questions, giving approximately $$5\frac{3}{4}$$ minutes to spend per question. The midterm will cover the content from the book sections:

• 2.1 - 2.4
• 3.1 - 3.3
• 4.1 - 4.3
• 5.1 - 5.3
• 6.1 - 6.4
• 7.1 - 7.2
• 8.1 - 8.3
• 10.1 - 10.2

The material will have a slightly stronger focus on the topics later in the course, with approximately:

• 4 questions on data summary and analysis.
• 3 questions on probability.
• 2 questions on binomial distributions.
• 2 questions on normal distributions and the central limit theorm.
• 3 questions on estimation and confidence intervals.
• 3 questions on hypothesis testing.
• 4 questions on correlation and regression.

There will be an emphasis on the following topics:

• Understanding and interpreting frequency distributions and their graphical analogs.
• Computing and interpreting the mean, median and mode. Computing and interpreting the coefficient of variation and z scores. You should also be able to compute a weighted mean or the mean from a frequency distribution.
• Summarizing data sets with percentiles. You should be able to produce a five number summary for a simple data set or interpret the analogous box plot.
• How to compute the probability of events from a table. You should be familiar with how to use the addition rule, the multiplication rule, “AND”, “OR”, complements and conditional probability to analyze these events.
• Independence and its relationship to sampling with and without replacement. You should be able to compute simple probabilities based on this.
• How to find the relevant parameters for the binomial distribution for a word problem. You need to identify the correct number of trials, the probability of success and the probability of failure.
• How to find the probability of randomly selecting an observation from a binomial distribution that is at least some value, at most some value, or lying in some range. You should also be able to identify if observing such a value is significantly high or significantly low, using a given $$\alpha$$ level of significance.
• How to find the probability of randomly selecting an observation from a normal distribution that is at least some value, at most some value, or lying in some range.
• How to use the Central Limit Theorem to find the probability of a sample mean being at least some value, at most some value, or lying in some range.
• How to find a $$t_\frac{\alpha}{2}$$ or a $$z_\frac{\alpha}{2}$$ critical value from the appropriate student t or standard normal distribution, given some level of confidence $$(1 - \alpha)\times 100\%$$.
• When to use a critical value from a student t distribution and when to use a critical value from a standard normal distribution. You should understand how many degrees of freedom to use in the student t when it is appropriate.
• How to compute a confidence interval for a population proportion or population mean, either directly in StatCrunch, or piece-by-piece using the appropriate critical value, point estimate and standard error.
• How to compute the margin of error for a confidence interval, either piece-by-piece using the appropriate critical value and standard error, or given a confidence interval.
• How to compute a point estimate for a population proportion or a population mean, either directly from sample values or given a confidence interval.
• How to find the necessary number of samples to estimate a population proportion or a population mean, given a target margin of error and given level of confidence.
• How to perform a hypothesis test for a population proportion or population mean given sample values, a level of significance and whether the population standard deviation is known or unknown. You should be able to conclude the hypothesis test correctly given the P-value from such a test.
• How to compute the P-value from a z score or t test statistic given a one-sided or two-sided hypothesis test. You should be able to infer what type of test statistic is being evaluated based on the use of a population proportion, a population mean, and whether the population standard deviation is known or not. You should be able to infer as well whether a left-sided, right-sided or two-sided test is being used.
• How to study scatter plots in StatCrunch with data sets like the Body Data (or other data sets) to examine for extreme outliers, nonlinear patterns, and linear trends.
• How to compute the linear correlation coefficient in StatCrunch with data sets like the Body Data (or other data sets), and when this is a good measure of the association between two variables – e.g., when is or is not the correlation significant, and when its interpretation affected by nonlinearity and extreme outliers.
• How to compute a prediction using a regression line in StatCrunch with data sets like the Body Data (or other data sets), and when is the prediction reliable. E.g. when should we refer instead to the mean value of the response for the prediction, in the case of nonlinearity, extreme outliers that have affected the fit of the regression line, the scope of the regression line, and when the correlation is not significant.

## Suggested problems

You are recommended to review all quiz and midterm questions. You can expect the final exam to have questions that are similar to these but not exact – remember, there are solutions available for these questions so final exam questions will not be verbatim. You will most likely need to practice the same skills from these problems, but sometimes questions in the final exam will ask you to do this in a novel way. Make sure you understand the methods used in these problems and how to perform the solutions on your own. Try solving simple variations on these problems.

In Pearson, there is an online final exam review – this is not scored for the final grade, and you can ignore problems that do not come from the above sections or topics.

In the textbook, you are recommended to study chapter review problems that emphasize the above topics.

In the lectures, you are recommended to study all discussion questions and examples that emphasize the above topics.

Because there is no partial credit, the midterm has a built in curve. The exam is graded out of 20 points, with 21 questions each worth 1 point. This means that
Number of questions incorrect Percent score
0 105%
1 100%
2 95%
3 90%
4 85%
5 80%
6 75%
7 70%
8 65%
9 60%
10 55%
11 50%
12 45%
13 40%
14 35%
15 30%
16 25%
17 20%
18 15%
19 10%
20 5%
21 0%