# Midterm 3 Study guide

## Instructions

The midterm will be available on Thursday April 23 from 12:00 AM until 11:59 PM. You may take the midterm at any time during this period in Canvas, but you will only have 75 minutes to complete this once it begins. The midterm will be a total of $$13$$ questions long giving approximately $$5\frac{3}{4}$$ minutes to spend per question. The midterm will cover the content from the book sections:

• 6.1 - 6.2
• 6.4 - 6.5
• 7.1 - 7.2
• 8.1 - 8.3

There will be an emphasis on the following topics:

• 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 assess the normality of some sample of observations using histograms or Q-Q plots.
• 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.

## Suggested problems

In Pearson, there is an online miderm 3 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.

You are recommended to review all quiz questions.

Because there is no partial credit, the midterm has a built in curve. The exam is graded out of 20 points, with 13 questions each worth 1.6 points. This means that
Number of questions incorrect Percent score
0 104%
1 96%
2 88%
3 80%
4 72%
5 64%
6 56%
7 48%
8 40%
9 32%
10 24%
11 16%
12 8%
13 0%