— MA121: Introduction to Statistics —

Read sections 2 and 3 from chapter 1. Section 2 provides a brief introduction to the field of statistics and some relevant examples. Section 3 presents more examples of how statistics can lend credibility to making arguments. Also, complete the questions in these sections.

Read sections 4 and 5 from chapter 1, and then complete the questions at the end of each section. Section 4 introduces descriptive statistics by using examples and discusses the difference between descriptive and inferential statistics. Section 5 talks about samples and populations, explains how one can identify biased samples, and defines differential statistics. 

Read section 1 from chapter 1 to further enhance your understanding of the elements of descriptive and inferential statistics. This section will introduce some of the key concepts in statistics and has numerous exercise and examples. Complete the odd-numbered exercises before checking the answers.

Read section 7 from chapter 1 and section 4 from chapter 6. Also, complete the questions at the end of each section. Section 7 will introduce several types of data and their distinguishing features. You will also learn about independent and dependent variables. Section 4 will explain how common data can be coded and collected. 

Study section 3 from chapter 1. This reading talks about ways that data can be presented. Attempt the odd-numbered exercises on page before checking the answers.

Read sections 3-7, 9, and 10 from chapter 2. Also, complete the questions at the end of each section. Section 3 provides an overview of the available methods to portray distributions of quantitative variables. Section 4 introduces you to the stem and leaf plot. In sections 5 and 6, you will learn how to capture the frequency of your data. Section 7 discusses box plots for the purpose of identifying outliers and for comparing distributions. Section 9 discusses bar charts for quantitative variables. Section 10 talks about the method of line graphs, which is based on bar graphs.

Read section 1 from chapter 2. This reading further elaborates on ways of describing data. In particular, you will learn about the relative frequency histogram. Complete the odd-numbered exercises on before checking the answers.

Read sections 2, 4, 8, 12, and 13 from chapter 3. Also, complete the questions at the end of each section. Section 2 defines the concept of central tendency. Section 4 introduces mean, median, and mode in the context of examples. Section 8 further elaborates on median and mean and discusses their strengths and weaknesses in measuring the central tendency. Section 12 addresses the concept of variability. Section 13 discusses range, interquartile range, variance, and the standard deviation. 

Read sections 2 and 3 from chapter 2. Section 2.2 further elaborates on mean, median, and mode - both at the population level and sample level. This section contains many interesting examples and exercises. Section 2.3 talks about range, variance, and standard deviation using many examples. Complete the odd-numbered problems in the exercise sets for each section before checking the answers.

Watch this video series, which begins with a discussion on descriptive statistics and inferential statistics and then talks about mean, median, and mode, as well as sample variance.

Read section 8 of chapter 1. Also, complete the questions at the end of the section. This reading discusses percentiles, which are useful for describing relative standings of observations in a dataset. This reading presents several definitions, so make sure to take notes.

Watch this video tutorial to learn how to create the scatter plot for bivariate data, using two variables x and y. It may be useful to review the definitions on this webpage.

Read sections 3, 5, and 6 from chapter 4. Also, complete the questions at the end of each section. Section 3 introduces Pearson's correlation and explains what the typical values represent. Section 5 further elaborates on the properties of r, particularly the fact that it is invariant under linear transformation. Section 6 introduces several formulas that can be used to compute Pearson's correlation.

Read sections 2 and 3 from chapter 5. Also, complete the questions at the end of each section. Section 2 talks about experiments for which outcomes are equally likely to occur and also discusses the frequency approach to assign probabilities. Section 3 focuses on the concept of events and also touches upon the issue of conditional probability.

Study chapter 3 to learn about basic concepts of probability. Section 1 discusses spaces, events, and their probabilities using many examples. Section 2 elaborates on sets operations, including complements, intersections, and unions using Venn diagrams. Section 3 introduces conditional probability and talks about independent events. Complete the odd-numbered exercises for each section before checking the answers.

Read section 6 from chapter 5. Also, complete the questions at the end of this section. Section 6 introduces formulas for combinations and permutations, which are useful to compute probabilities.

Watch these videos, which introduce Venn diagrams in the context of playing cards and discuss the addition rule for probability.

Read sections 1 and 2 from chapter 4. Section 1 defines discrete and continuous random variables. Section 2 introduces the distributions for discrete random variables. This section also talks about the mean and variance calculations. Complete the odd-numbered exercises for each section before checking the answers.

Watch these videos on binomial distributions. The first explains how to compute the mean of a binomial distribution. The next two videos introduce binomial probabilities and show how to graph them. The remaining videos elaborate on binomial distribution in the context of basketball examples.

Read sections 8, 10, and 11 from chapter 5. Also, complete the questions at the end of each section. Section 8 talks about binomial probabilities, discusses how to compute their cumulatives, and introduces the mean and standard deviation. Section 10 introduces the Poisson probability formula. Section 11 defines multinomial outcomes and discusses how to compute probabilities by using the multinomial distribution.

Note: For Section 8, the link to the Binomial Calculator part way down the page may not work. If so, you can instead use this Binomial Calculator.

Read section 2 from chapter 5. This section talks about standard normal curve and how to compute certain areas underneath the curve. This section also contains numerous exercises and examples. Complete the odd-numbered exercises for this section before checking the answers.

Read sections 3, 4, 6, and 7 from chapter 7. Also, complete the questions at the end of each section. Section 3 briefly talks about the history of both the normal distribution and the central limit theorem, and this section also discusses the relation of normal distributions to errors. Section 4 discusses ways of computing the areas under the normal curve. Section 6 discusses the standard normal distribution and the related areas under the standard normal curve. Regarding the calculation of areas, Section 6 also discusses how to translate from non-standard normal to standard normal. Section 7 addresses how to compute (cumulative) binomial probabilities by using normal approximations.

Watch this video on normal distribution. This video introduces normal distribution and its density curve and explains how to read the areas underneath the normal curve. It also touches on the central limit behavior.

From chapter 5, read section 1, section 3, and section 4. Section 1 talks about how to describe continuous distributions and compute related probabilities, including some basic facts about the normal distribution. Section 3 talks about how to compute probabilities related to any normal random variable. This section has many examples illustrating the usage of z-score transformations. Section 4 defines tail probabilities and illustrates how to find them. Complete the odd-numbered exercises at the end of each section before checking the answers.

Read section 2 from chapter 9. Also, complete the questions at the end. Section 2 introduces sampling distribution by using a concrete, discrete example, followed by a continuous example. This section also discusses sampling distributions' relationship to inferential statistics.

Use the information provided on the demonstration pages and interact with the various simulations.

If you have not done so already, you will need to download install the free Wolfram CDF Player™. If using Chrome as your browser, you will also need to download the CDF files from the pages linked to above, and run them through the CDF Player on your desktop. Other browsers will allow you to interact with the demonstrations directly on the webpage.

Read sections 6 and 7 from chapter 9. Also, complete the questions at the end of each section. Section 6 discusses the mean and variance of the sampling distribution of the mean. This section also shows how central limit theorem can help to approximate the corresponding sampling distributions. Section 7 talks about the properties of the sampling distribution for differences between means by giving the formulas of both mean and variance for the sampling distribution. Using the central limit theorem, it also talks about how to compute the probability of a difference between means being beyond a specified value.

Read sections 1 and 2 from chapter 6 . Section 1 presents several concrete examples to calculate the exact distributions of the sample mean. Based on these distributions, the corresponding means and standard deviations are computed for demonstrations. Section 2 concerns the sampling distributions of the sample means when the sample size is large. The case when the population is normal is also considered. The central limit theorem is used for large sample approximations. Complete the odd-numbered exercises at the end of each section before checking the answers.

Watch these videos, which discuss sampling distributions.

Read section 8 from chapter 9. Also, complete the questions at the end. Section 8 talks about how the shape of the sampling distribution of Pearson correlation deviates from normality and then discusses how to transform r to a normally distributed quantity. Furthermore, this section talks about how to calculate the probability of obtaining an r above a specified value.

Read section 9 from chapter 9. Also, complete the questions at the end. Section 9 introduces the mean and standard deviation of the sampling distribution of p, and this section discusses the relationship between the sampling distribution of p and the normal distribution.

To enhance your understanding, watch this video on determining standard deviation.

Read sections 2 and 3 from Chapter 10. Also, complete the questions in each section. Section 2 explains the basic concepts of sample statistics and population parameters as well as the basic goal of estimation for which point estimates and interval estimates are introduced. Section 3 talks about the degree of freedom, which is defined as the number of independent pieces of information on which a point estimate is based. Section 3 also talks about variance, a quantity depending on the degrees of freedom.

Read section 4 from Chapter 10. Also, complete the questions at the end. Section 4 discusses two important characteristics used as point estimates of parameters: bias and sampling variability. Bias refers to whether an estimator tends to over or underestimate the parameter. Sampling variability refers to how much the estimate varies from sample to sample.

Read sections 7, 8, 9, and 11 from Chapter 10. Also, answer the questions at the end of each section. Section 7 explains the need for confidence intervals and why a confidence interval is not the probability the interval contains the parameter. Section 8 explains how to compute a confidence interval on the mean when sigma is unknown and needs to be estimated. For this purpose, it also explains when to use t-distribution or a normal distribution. Section 9 states the difference between the shape of the t distribution and the normal distribution, and this section also explains how this difference is affected by degrees of freedom. Section 11 explains the procedure to compute a confidence interval on the difference between means.

This lab will help you develop a basic understanding of the properties of a sampling distribution, based on the properties of the population. Review the illustrated instructions, and follow the general instructions to learn more about confidence interval simulations.

Then, use the Wolfram Demonstration provided in the next resource for a more interactive practice of the topics covered here.

Note: Running the actual Online Statistics Education simulation yourself will likely not work, as the Java format that it is is no longer supported by most browsers.

The demonstration provided here is a supplement to the reading above. Use the information provided on the demonstration page and interact with the simulation. If you prefer to watch a video of this simulation, you may do so here.

Note: If you have not done so already, you will need to download install the free CDF Player from the Wolfram Demonstrations Project. If using Chrome as your browser, you will also need to download the CDF file from the page linked to above, and run it through the CDF Player on your desktop. Other browsers will allow you to interact with the demonstration directly on the webpage.

Read the instructions and watch the video demo in order to see how the degrees of freedom affect the difference between t and normal distributions.

Note: Running the actual simulation yourself will likely not work, as the Java format that it is in is no longer supported by most browsers. Instead, you may use the Wolfram Demonstrations provided below for a more interactive practice of the topics covered here.

The demonstration provided here are a supplement to the readings and videos above. Use the information provided on the demonstration page and interact with the simulation. If you prefer to watch a video of this simulation, you may do so here.

Note: If you have not done so already, you will need to download install the free CDF Player from the Wolfram Demonstrations Project. If using Chrome as your browser, you will also need to download the CDF file from the page linked to above, and run it through the CDF Player on your desktop. Other browsers will allow you to interact with the demonstration directly on the webpage.

Read sections 12 and 13 from Chapter 10. Also, complete the questions at the end of each section. Section 12 shows how to compute a confidence interval for Pearson's correlation; the solution lies in using Fisher's z transformation. Section 13 explains the procedure to compute confidence intervals for population proportions, where the sampling distribution needs a normal approximation.

Watch these two videos, which discuss confidence intervals.

Read sections 2, 4, and 5 from Chapter 11, and complete the questions at the end of each section. Section 2 discusses the logic behind hypothesis testing using concrete examples and explains how to set up null and alternative hypothesis. Section 4 explains what Type I and II errors are and how they can occur. Section 5 introduces one-tailed and two-tailed tests and explains which one should be used for the testing purpose.

Read section 3 from Chapter 8. This section explains what the observed significance of a test is; in particular, this reading tells us how to compute it and use it in the p-value approach. Study the examples, and complete the odd-numbered exercises at the end of the section before checking the answers.

Read sections 6 and 7 from Chapter 11, and complete the questions at the end of each section. Section 6 discusses whether rejection of the null hypothesis should be an all-or-none proposition. Section 7 discusses how to interpret non-significant results; for example, it explains why the null hypothesis should not be accepted, or accepted with caution. This section also describes how a non-significant result can increase confidence that the null hypothesis is false.

Read this section, which discusses two types of errors in hypothesis testing, using numerous examples.

Watch these videos on hypothesis testing.

Read sections 8 and 9 from Chapter 11. Also, complete the questions at the end of each section. Section 8 lists four key steps in hypothesis testing. Section 9 explains the close relationship between confidence intervals and significance tests.

Watch the videos titled "Significance Level in Hypothesis Testing" and "Hypothesis Testing Example." The first video shows you how to make a decision in a hypothesis test based on the significance level of critical values. The second video provides an example of a left tailed hypothesis test.

Read section 2 from Chapter 12. This section shows how to test the null hypothesis that the population mean is equal to some hypothesized value, using a very concrete example. In this example, all the main elements of hypothesis testing come in to play a role. There are 9 questions at the end of the section to help your understanding of the material.

Read section 2, section 4, and 5. Complete the odd-numbered problems at the end of each section before checking your answers.

Section 2 talks about how to use the central limit theorem to test a population mean when the sample size is large. It also addresses how to interpret the test results in the application background. Section 4 discusses testing a population mean when the sample size is small. This section outlines a five-step testing procedure and then illustrates this procedure with an example. Study the example carefully and complete the relevant exercises and applications. Section 5 talks about large sample tests for a population proportion. Both the critical value and p-value approach are introduced based on a standardized test statistic. Once again, this section illustrates the five-step testing procedure in Examples 12-15.

Read section 4 from Chapter 12. Also, answer the questions at the end of this section. This section covers how to test for differences between means from two separate groups of subjects. This reading presents an example of opinions on animal research, and the main interest is to test for gender difference at the population level. The detailed testing procedure is carried out by using the standard steps in hypothesis testing.

Watch these videos on the difference of means.

Read this section, which discusses contingency tables, and answer the questions at the end of the section. While this section is optional, studying it may help you if you wish to take the credit-aligned exam that is linked with this course.

Read these two sections, which discuss chi-square distributions and how to test goodness of fit. Also, answer the questions at the end of each section. While these sections are optional, studying them may help you if you wish to take the credit-aligned exam that is linked with this course.

Watch these videos, which discuss chi-square distributions, goodness of fit, and contingency tables.

Watch these videos, which discuss comparing population proportions. While these videos are optional, studying these topics may help you if you are interested in taking the credit-aligned exam that is linked with this course.

Read section 2 from Chapter 14. Also, answer the questions at the end. Section 2 defines simple linear regression, introduces scatter plot to reveal linear patterns, and then talks about prediction error. This section also talks about how to compute regression line by minimizing squared errors.

Read these sections on linear regression. Linear regression, the simplest form of regression, is used to obtain a linear relationship between two variables.

Be sure to click "next" and read each section.

Read these sections on correlation. You will learn the interpretation and calculation of the correlation coefficient, how to test its significance, and the relation between correlation and causation.

Be sure to click "next" and read each section.

Read section 2 of Chapter 10 for a discussion on linear correlation. You will learn what the linear correlation coefficient is, how to compute it, and what it tells us about the relationship between two variables x and y.

Read section 4 from Chapter 14. Also, answer the questions at the end of the section. Section 4 further discusses the sums of squares, including partitioning sum of squares into sums of squares predicted and sum of squares error. 

Watch these videos, which discuss the regression line.

Read section 5 from Chapter 14. Also, answer the questions at the end. Section 5 discusses how to compute the standard error of the estimate based on errors of prediction as well as how to compute the standard error of the estimate based on a sample.

Read section 6 from Chapter 14. Also, answer the questions at the end. Section 6 starts with assumptions on the errors that are necessary for statistical inference. Then, this reading shows an example of a significance test for the slope. This section also talks about constructing confidence intervals for the slope. Then, it closes with a significance test for the correlation.

Read section 5 from Chapter 10. This section further details two types of inferences on the slope parameter, considering both confidence intervals and hypothesis testing. Complete the odd-numbered exercises at the end of the section before checking your answers.

Read section 7 from Chapter 14. Also, answer the questions at the end. Section 7 discusses the notion of influence and describes what makes a point influential. It further introduces the concepts of leverage and distance, which are useful to detect influential observations.

Read section 8 from Chapter 10. This section presents a complete example on linear regression, starting from presenting the data, then proceeds to a scatter plot to identify the linear pattern, and fits a linear model using least squares estimation. This reading also addresses some statistical inferences on both correlation coefficient and slope parameter. Complete the odd-numbered exercises at the end of the section before checking the answers.

Watch these videos, which discuss each of the steps in ANOVA. While these videos are optional, studying ANOVA may help you if you are interested in taking the credit-aligned exam that is linked with this course.

Read this chapter and complete the questions at the end of each section. While these sections are optional, studying ANOVA may help you if you are interested in taking the credit-aligned exam that is linked with this course.