index.Rmd

---
title: "Textbook Home Page"
output: 
  html_document:
    theme: cerulean
    toc: true
    toc_float: false
---

<script type="text/javascript">
 function showhide(id) {
    var e = document.getElementById(id);
    e.style.display = (e.style.display == 'block') ? 'none' : 'block';
 }
</script>

**Welcome to Math 221**

This textbook contains 24 lessons divided into four units. The first unit establishes the Statistical Process and some theoretical foundations for working with quantitative data. The second unit applies these theoretical concepts to real world data analysis with quantitative data. The third unit does the same, but with categorical data. The final unit takes a look at bivariate data by studying scatterplots, correlation, and simple linear regression.


<br/>

<div class="mboxfull">
<a href="javascript:showhide('Unit1')"><div class="mbox usermessage">Unit 1: Quantitative Data <span style="font-size:8pt;float:right;padding:5px;">Click to Expand</span></div></a>

<div id="Unit1" style="display:none;">

<table class="tmain">
<tr>
<td><p>[Lesson 1: (On Campus) Course Intro & Probability](Lesson01_Campus.html) <a href="javascript:showhide('lesson01_Campus_Outcomes')"><span style="font-size:8pt;float:right;">Show Outcomes</span></a>
<div id="lesson01_Campus_Outcomes" style="display:none;">
By the end of this lesson, you should be able to:

- Understand and explain the course policies
- Access course resources (course outline, lesson schedule, preparation activities, reading quizzes, homework assignments, assessments, Zoom, etc.)
- Communicate with your instructor
- Obtain access to a spreadsheet program (Microsoft Excel)
- Discuss ways in which you will apply gospel principles to your work in this class
</div>
</p></td>
</tr>
<tr>
<td><p>[Lesson 1: (Online) Course Intro & Probability](Lesson01.html) <a href="javascript:showhide('lesson01_Online_Outcomes')"><span style="font-size:8pt;float:right;">Show Outcomes</span></a>
<div id="lesson01_Online_Outcomes" style="display:none;">
By the end of this lesson, you should be able to:

* Understand and explain the course policies
* Access course resources (course outline, lesson schedule, preparation activities, reading quizzes, homework assignments, assessments, Zoom, etc.)
* Communicate with your instructor
* Obtain access to a spreadsheet program (Microsoft Excel)
* Discuss ways in which you will apply gospel principles to your work in this class
* State and apply the three rules of probability.
</div>
</p></td>
</tr>
<td><p>[Lesson 1: (World Wide Block) Course Intro & Probability](Lesson01_WWB.html) <a href="javascript:showhide('lesson01_WWB_Outcomes')"><span style="font-size:8pt;float:right;">Show Outcomes</span></a>
<div id="lesson01_WWB_Outcomes" style="display:none;">
By the end of this lesson, you should be able to:

* Understand and explain the course policies
* Access course resources (course outline, lesson schedule, preparation activities, reading quizzes, homework assignments, assessments, Zoom, etc.)
* Communicate with your instructor
* Obtain access to a spreadsheet program (Microsoft Excel)
* Discuss ways in which you will apply gospel principles to your work in this class
* State and apply the three rules of probability.
</div>
</p></td>
</tr>
<tr class="alt">
<td><p>[Lesson 2: The Statistical Process & Design of Studies](Lesson02.html) <a href="javascript:showhide('lesson02_Outcomes')"><span style="font-size:8pt;float:right;">Show Outcomes</span></a>
<div id="lesson02_Outcomes" style="display:none;">
By the end of this lesson, you should be able to:

* State the five steps of the Statistical Process
* Distinguish between an observational study and an experiment.
* Distinguish between a population and a sample.
* Distinguish between a categorical and a quantitative variable.
* Distinguish and give an example of each of the following sampling schemes:
  + Simple random sampling
  + Systematic sampling
  + Cluster sampling
  + Stratified sampling
  + Convenience sampling
* Explain the significance of using a random sample.
</div>
</p></td>
</tr>
<tr>
<td><p>[Lesson 3: Describing Quantitative Data (Shape & Center)](Lesson03.html) <a href="javascript:showhide('lesson03_Outcomes')"><span style="font-size:8pt;float:right;">Show Outcomes</span></a>
<div id="lesson03_Outcomes" style="display:none;">

By the end of this lesson, you should be able to:

* Determine the shape of a distribution using a histogram.
* Interpret the mean, median, and mode for quantitative data.
* Apply the Excel functions AVERAGE, MEDIAN, and MODE when working with quantitative data in Excel.
* Determine the location of the mean relative to the median of left-skewed, right-skewed, or bell-shaped distributions visually using a histogram.
* Interpret a histogram.  
* Distinguish between a parameter and a statistic.
</div>
</p></td>
</tr>
<tr class="alt">
<td><p>[Lesson 4: Describing Quantitative Data (Spread)](Lesson04.html) <a href="javascript:showhide('lesson04_Outcomes')"><span style="font-size:8pt;float:right;">Show Outcomes</span></a>
<div id="lesson04_Outcomes" style="display:none;">

By the end of this lesson, you should be able to:

* Approximate the standard deviation of a distribution visually from a bell-shaped histogram.
* Calculate the standard deviation from quantitative data using Excel.
* Interpret the standard deviation for symmetric distributions. 
* Properly apply the Excel functions STDEV.S, PERCENTILE.INC, QUARTILE.INC, MIN, and MAX to quantitative data.
* Interpret the five-number summary for quantitative data.
* Create a box-plot from quantitative data using Excel. 
* Determine the five-number summary visually from a box plot. * Explain the relationship between probabilities, percentiles, and percentages.

</div>
</p></td>
</tr>
<tr>
<td><p>[Lesson 5: Normal Distributions](Lesson05.html) <a href="javascript:showhide('lesson05_Outcomes')"><span style="font-size:8pt;float:right;">Show Outcomes</span></a>
<div id="lesson05_Outcomes" style="display:none;">

By the end of this lesson, you should be able to:

* State the properties of a normal density curve.
* Calculate the z-score of an individual observation, given the mean and standard deviation.
* Interpret a z-score.
* Calculate probability as area under a normal density curve.
* Calculate a percentile using the normal distribution.

</div>
</p></td>
</tr>
<tr class="alt">
<td><p>[Lesson 6: Distribution of Sample Means & The Central Limit Theorem](Lesson06.html) <a href="javascript:showhide('lesson06_Outcomes')"><span style="font-size:8pt;float:right;">Show Outcomes</span></a>
<div id="lesson06_Outcomes" style="display:none;">

By the end of this lesson, you should be able to:

*  Explain how a sampling distribution is created.
*  Determine the mean, standard deviation and shape of a distribution of sample means.
*  State and apply the Central Limit Theorem and the Law of Large Numbers.

</div>
</p></td>
</tr>
<tr>
<td><p>[Lesson 7: Calculating Probabilities involving the Sample Mean](Lesson07.html) <a href="javascript:showhide('lesson07_Outcomes')"><span style="font-size:8pt;float:right;">Show Outcomes</span></a>
<div id="lesson07_Outcomes" style="display:none;">

By the end of this lesson, you should be able to:

*  Calculate probabilities using a distribution of sample means.

</div>
</p></td>
</tr>
<tr class="alt">
<td><p>[Lesson 8: Review for Exam 1](Lesson08.html) <a href="javascript:showhide('lesson08_Outcomes')"><span style="font-size:8pt;float:right;">Show Outcomes</span></a>
<div id="lesson08_Outcomes" style="display:none;">

Unit 1 Review. The expectation on the Unit 1 Exam is that you should be able to do the following:

- Distinguish between a categorical and a quantitative variable.
- Distinguish between an observational study and an experiment.
- Distinguish between a population and a sample.
- Distinguish between a parameter and a statistic.
- Distinguish and give an example of each of the following sampling schemes:

  + Simple random sampling
  + Systematic sampling
  + Cluster sampling
  + Stratified sampling
  + Convenience sampling

- Explain the significance of using a random sample.
- Determine the shape of a distribution using a histogram and/or boxplot.
- Determine the centers of a given histogram and/or boxplot. 
- Identify the mean, median and standard deviation in skewed or normal histograms.
- Calculate the mean, median and standard deviation from quantitative data.
- Calculate a percentile from a quantitative data set.
- Calculate a five-number summary from quantitative data with Excel, or by hand.
- Create a histogram and a boxplot from quantitative data. 
- State and apply the three axioms of probability.
- State the properties of a normal density curve.
- Calculate the z-score of an individual observation, given the mean and standard deviation.
- Interpret a z-score.
- Calculate probability as area under a normal density curve.
- Assess normality using a histogram.
- Explain how a sampling distribution is created.
- Determine the mean, standard deviation, and shape of a distribution of sample means.
- State and apply the Central Limit Theorem and the Law of Large numbers.
- Calculate probabilities using a distribution of sample means.
</div>
</p></td>
</tr>
</table>

</div>
</div>

<br/>

<div class="mboxfull">
<a href="javascript:showhide('Unit2')"><div class="mbox usermessage">Unit 2: Quantitative Data <span style="font-size:8pt;float:right;padding:5px;">Click to Expand</span></div></a>

<div id="Unit2" style="display:none;">

<table class="tmain">
<tr>
<td><p>[Lesson 9: Inference for One Mean with Sigma Known (Hypothesis Test)](Lesson09.html) <a href="javascript:showhide('lesson09_Outcomes')"><span style="font-size:8pt;float:right;">Show Outcomes</span></a>
<div id="lesson09_Outcomes" style="display:none;">

By the end of this lesson, you should be able to:

- Conduct a Hypothesis Test for a single mean with σ known:
  + State the null and alternative hypothesis. 
  + Calculate the test-statistic and p-value of the hypothesis test.
  + Assess the statistical significance by comparing the p-value to the α-level.
  + Check the requirements for the hypothesis test.
  + Show the appropriate connections between the numerical and graphical summaries that support this hypothesis test. 
  + Draw a correct conclusion for the hypothesis test.
  + Interpret a Type I and II error.

</div>
</p></td>
</tr>
<tr class="alt">
<td><p>[Lesson 10: Inference for One Mean with Sigma Known (Confidence Interval)](Lesson10.html) <a href="javascript:showhide('lesson10_Outcomes')"><span style="font-size:8pt;float:right;">Show Outcomes</span></a>
<div id="lesson10_Outcomes" style="display:none;">

By the end of this lesson, you should be able to:

* Calculate and interpret a confidence interval for a population mean given a confidence level.
* Explain how the margin of error changes with the sample size and the level of confidence. 
* Identify a point estimate and margin of error for the confidence interval.
* Show the appropriate connections between the numerical and graphical summaries that support this confidence interval. 
* Check the requirements of the confidence interval.
* Calculate a desired sample size given a level of confidence and margin of error. 
</div>
</p></td>
</tr>
<tr>
<td><p>[Lesson 11: Inference for One Mean (Sigma Unknown)](Lesson11.html) <a href="javascript:showhide('lesson11_Outcomes')"><span style="font-size:8pt;float:right;">Show Outcomes</span></a>
<div id="lesson11_Outcomes" style="display:none;">

By the end of this lesson, you should be able to do the following with regards to confidence intervals and hypothesis testing.

**Regarding Confidence Intervals for a single mean with $\sigma$ unknown:**

* Calculate and interpret a confidence interval for a population mean given a confidence level.
* Identify a point estimate and margin of error for the confidence interval.
* Show the appropriate connections between the numerical and graphical summaries that support the confidence interval. 
* Check the requirements the confidence interval.
 
**Regarding Hypothesis Testing for a single mean with $\sigma$ unknown:**

* State the null and alternative hypothesis. 
* Calculate the test-statistic, degrees of freedom and p-value of the hypothesis test.
* Assess the statistical significance by comparing the p-value to the α-level.
* Check the requirements for the hypothesis test.
* Show the appropriate connections between the numerical and graphical summaries that support the hypothesis test. 
* Draw a correct conclusion for the hypothesis test.

</div>
</p></td>
</tr>
<tr class="alt">
<td><p>[Lesson 12: Inference for the Mean of Differences (Two Dependent Samples)](Lesson12.html) <a href="javascript:showhide('lesson12_Outcomes')"><span style="font-size:8pt;float:right;">Show Outcomes</span></a>
<div id="lesson12_Outcomes" style="display:none;">

By the end of this lesson, you should be able to do the following.

**Regarding Confidence Intervals for the mean of differences with dependent samples: **

- Calculate and interpret a confidence interval for the mean of differences given a confidence level.
- Identify a point estimate and margin of error for the confidence interval.
- Show the appropriate connections between the numerical and graphical summaries that support the   confidence interval.
- Check the requirements for the confidence interval.
  
**Regarding Hypothesis Testing for the mean of differences with dependent samples:**

  * State the null and alternative hypothesis. 
  * Calculate the test-statistic, degrees of freedom and p-value of the hypothesis test.
  * Assess the statistical significance by comparing the p-value to the α-level.
  * Check the requirements for the hypothesis test.
  * Show the appropriate connections between the numerical and graphical summaries that support the hypothesis test. 
  * Draw a correct conclusion for the hypothesis test.

</div>
</p></td>
</tr>
<tr>
<td><p>[Lesson 13: Inference for the Difference of Means (Two Independent Samples)](Lesson13.html) <a href="javascript:showhide('lesson13_Outcomes')"><span style="font-size:8pt;float:right;">Show Outcomes</span></a>
<div id="lesson13_Outcomes" style="display:none;">

</div>
</p></td>
</tr>
<tr class="alt">
<td><p>[Lesson 14: Inference with ANOVA (Several Independent Samples)](Lesson14.html) <a href="javascript:showhide('lesson14_Outcomes')"><span style="font-size:8pt;float:right;">Show Outcomes</span></a>
<div id="lesson14_Outcomes" style="display:none;">

</div>
</p></td>
</tr>
<tr>
<td><p>[Lesson 15: Review for Exam 2](Lesson15.html) <a href="javascript:showhide('lesson15_Outcomes')"><span style="font-size:8pt;float:right;">Show Outcomes</span></a>
<div id="lesson15_Outcomes" style="display:none;">

</div>
</p></td>
</tr>
</table>

</div>
</div>


<br/>

<div class="mboxfull">
<a href="javascript:showhide('Unit3')"><div class="mbox usermessage mw-customtoggle-Unit02">Unit 3: Categorical Data <span style="font-size:8pt;float:right;padding:5px;">Click to Expand</span></div></a>

<div id="Unit3" style="display:none;">

<table class="tmain">
<tr>
<td><p>[Lesson 16: Describing Categorical Data: Proportions; Sampling Distribution of a Sample Proportion](Lesson16.html) <a href="javascript:showhide('lesson16_Outcomes')"><span style="font-size:8pt;float:right;">Show Outcomes</span></a>
<div id="lesson16_Outcomes" style="display:none;">

</div>
</p></td>
</tr>
<tr class="alt">
<td><p>[Lesson 17: Inference for One Proportion](Lesson17.html) <a href="javascript:showhide('lesson17_Outcomes')"><span style="font-size:8pt;float:right;">Show Outcomes</span></a>
<div id="lesson17_Outcomes" style="display:none;">

</div>
</p></td>
</tr>
<tr>
<td><p>[Lesson 18: Inference for Two Proportions](Lesson18.html) <a href="javascript:showhide('lesson18_Outcomes')"><span style="font-size:8pt;float:right;">Show Outcomes</span></a>
<div id="lesson18_Outcomes" style="display:none;">

</div>
</p></td>
</tr>
<tr class="alt">
<td><p>[Lesson 19: Inference for Independence of Categorical Data](Lesson19.html) <a href="javascript:showhide('lesson19_Outcomes')"><span style="font-size:8pt;float:right;">Show Outcomes</span></a>
<div id="lesson19_Outcomes" style="display:none;">

</div>
</p></td>
</tr>
<tr>
<td><p>[Lesson 20: Review for Exam 3](Lesson20.html) <a href="javascript:showhide('lesson20_Outcomes')"><span style="font-size:8pt;float:right;">Show Outcomes</span></a>
<div id="lesson20_Outcomes" style="display:none;">

</div>
</p></td>
</tr>
</table>

</div>
</div>


<br/>

<div class="mboxfull">
<a href="javascript:showhide('Unit4')"><div class="mbox usermessage mw-customtoggle-Unit02">Unit 4: Bivariate Data <span style="font-size:8pt;float:right;padding:5px;">Click to Expand</span></div></a>

<div id="Unit4" style="display:none;">

<table class="tmain">
<tr>
<td><p>[Lesson 21: Describing Bivariate Data: Scatterplots, Correlation, & Covariance](Lesson21.html) <a href="javascript:showhide('lesson21_Outcomes')"><span style="font-size:8pt;float:right;">Show Outcomes</span></a>
<div id="lesson21_Outcomes" style="display:none;">

</div>
</p></td>
</tr>
<tr class="alt">
<td><p>[Lesson 22: Simple Linear Regression](Lesson22.html) <a href="javascript:showhide('lesson22_Outcomes')"><span style="font-size:8pt;float:right;">Show Outcomes</span></a>
<div id="lesson22_Outcomes" style="display:none;">

</div>
</p></td>
</tr>
<tr>
<td><p>[Lesson 23: Inference for Bivariate Data](Lesson23.html) <a href="javascript:showhide('lesson23_Outcomes')"><span style="font-size:8pt;float:right;">Show Outcomes</span></a>
<div id="lesson23_Outcomes" style="display:none;">

</div>
</p></td>
</tr>
<tr class="alt">
<td><p>[Lesson 24: Review for Exam 4](Lesson24.html) <a href="javascript:showhide('lesson24_Outcomes')"><span style="font-size:8pt;float:right;">Show Outcomes</span></a>
<div id="lesson24_Outcomes" style="display:none;">

</div>
</p></td>
</tr>
</table>

</div>
</div>