Before we dive into the topics covered in this module, it's important to evaluate your current understanding of AP Statistics. Take this pre-assessment quiz to gauge your knowledge and pinpoint areas where you may need to focus your study.
Once you've completed the quiz, review your results and identify the topics where you scored the lowest. Concentrate on these topics during the rest of the module.
In the Pre-Assessment Quiz, you will be asked a series of multiple-choice questions that cover a range of topics in AP Statistics. The quiz is designed to help you evaluate your current knowledge and identify areas where you may need to focus your study. Once you've completed the quiz, you will be able to review your results and see which topics you need to work on. This will help you get the most out of the rest of the module and be better prepared for future studies in AP Statistics.
- Question 1: What is the difference between a population and a sample?
[( )] A population is a subset of a sample [(X)] A population includes all individuals of interest, while a sample is a subset of the population [( )] A sample is larger than a population [( )] There is no difference between a population and a sample
[[?]] Consider the context of data collection and analysis [[?]] Which term refers to the entire group of interest, and which refers to a smaller portion?
- Question 2: What does a p-value represent?
[(X)] The probability of observing a test statistic as extreme or more extreme than the one observed, given that the null hypothesis is true [( )] The probability of the null hypothesis being true [( )] The probability of the alternative hypothesis being true [( )] The probability of observing a test statistic as extreme or more extreme than the one observed, given that the alternative hypothesis is true
[[?]] Reflect on the role of a p-value in hypothesis testing [[?]] Remember that the p-value is used to make decisions about the null hypothesis
- Question 3: What is the purpose of a confidence interval?
[(X)] To estimate a population parameter with a certain level of confidence [( )] To test a hypothesis about a population mean or proportion [( )] To calculate the probability of observing a particular sample [( )] To determine the sample size needed for a study
[[?]] Think about the concept of confidence in the context of estimation [[?]] Recall that a confidence interval provides a range of plausible values for a population parameter
- Question 4: Which of the following is not a condition for performing a t-test?
[( )] Independence [( )] Normality of the sample [(X)] Random sampling [( )] Approximately normal population distribution
[[?]] Review the assumptions made when performing a t-test [[?]] Recall that a t-test is used when the population standard deviation is unknown
- Question 5: When should a chi-square test be used?
[( )] When the data is continuous and normally distributed [(X)] When the data is categorical and the samples are independent [( )] When the data is ordinal and the samples are dependent [( )] When the data is normally distributed and the population standard deviation is known
[[?]] Think about the types of data appropriate for a chi-square test [[?]] Remember the assumptions made when performing a chi-square test
- Question 6: What is the purpose of a Type I error?
[(X)] Rejecting a true null hypothesis [( )] Failing to reject a false null hypothesis [( )] Accepting a true alternative hypothesis [( )] Failing to reject a true null hypothesis
[[?]] Consider the relationship between Type I errors and hypothesis testing [[?]] Recall that Type I errors are associated with false rejections
- Question 7: What is the coefficient of determination (R²)?
[(X)] The proportion of the total variation in the dependent variable that is explained by the independent variable [( )] The square of the correlation coefficient [( )] The ratio of the explained variation to the unexplained variation [( )] The strength and direction of a linear relationship between two variables
[[?]] Reflect on the purpose of the coefficient of determination in the context of regression [[?]] Remember that R² is used to measure the goodness of fit of a regression model
- Brief overview of the assignment
- Importance of reading and understanding each question
- Guidance on the format of responses: using an Excel page
- Adding a new column to the database for annual sales
- Calculation methods for obtaining annual sales (Square feet * Sales per square foot)
- Calculating mean, standard deviation, skew, and interquartile range
- Using built-in Excel formulas for each calculation:
- Mean:
AVERAGE(range) - Standard Deviation:
STDEV.S(range) - Skew:
SKEW(range) - Interquartile Range:
QUARTILE.INC(range, 3) - QUARTILE.INC(range, 1)
- Mean:
- Replicating formulas across columns in Excel
- Procedure to create a boxplot for the annual sales variable
- How to adjust the placement of the boxplot
- Interpreting boxplots and identifying outliers
- Procedure to create a histogram for the sales per square foot variable
- Customizing the histogram, including adjusting the chart title
- Interpretation of histograms, including assessing symmetry and skewness
- Location and format for written answers in Excel
- Importance of addressing each part of each question
- Examples of questions to be answered (distribution, skewness, outliers)
- Point value assigned to each question
- Importance of fully addressing each question to earn maximum points
- Encouragement to ask questions or seek clarification as needed
- Instructor’s wishes for student success on the assignment
- Purpose and relevance of scatter plots and regression analysis in data interpretation.
- Choosing appropriate variables for analysis: dependent and independent variables.
- Example with bachelor's degree vs sales per square foot.
- How to create a scatter plot using Excel:
- Selecting relevant data.
- Navigating to the "Insert" tab.
- Choosing scatter plot from the available chart options.
- Steps to add trend line to the scatter plot.
- Configuring trend line options:
- Displaying equation on the chart.
- Displaying R square value on the chart.
- Interpreting the R square value and regression equation.
- Significance and implications of these results in a sample data set.
- Navigating to the Data Analysis ToolPak in Excel.
- Choosing "Regression" from the list of available analysis tools.
- Selecting y-axis (dependent variable) and x-axis (independent variable).
- Observing output of regression analysis, including R square value, model, intercept and slope.
- Example calculation to predict the future value of y based on a given independent variable value.
- Explanation of t-statistics and p-value.
- Hypothesis testing using p-value:
- Criteria for rejecting or failing to reject null hypothesis.
- Interpretation of results in this context.
- Explanation of significance level for the entire model.
- Conditions for rejecting or failing to reject null hypothesis regarding model significance.
- Final words and encouragement to use personal data sets for practice.
- Definition and purpose of hypothesis testing.
- Explanation of null and alternative hypotheses.
- Understanding the concept of a Type I and Type II error.
- Importance of the significance level and its implication in hypothesis testing.
- One-sample Z-test and T-test: When and why to use them.
- Independent samples T-test: Understanding its application and interpretation.
- Paired sample T-test: Knowing when it is appropriate and how to interpret the results.
- Chi-square test: Understanding its use in categorical data.
- Step-by-step walkthrough of performing a Z-test, including data arrangement, formula application, and interpretation.
- Detailed guide on conducting a T-test with practical examples.
- Hands-on practice with Chi-square test using a sample dataset.
- Explaining potential errors and misinterpretations when performing hypothesis tests.
- Interpreting the results of a hypothesis test: Understanding the p-value and test statistic.
- Making decisions based on the results of a hypothesis test: Rejecting or failing to reject the null hypothesis.
- Understanding the practical implications of these decisions in a real-world context.
- Proper formatting and presentation of the results from a hypothesis test.
- Writing a summary and conclusion based on the results of a hypothesis test.
- Understanding how to clearly communicate these findings to a non-technical audience.
- Review key concepts and terminologies from the week's material.
- Complete practice problems and exercises related to hypothesis testing.
- Review and discuss solutions to practice problems.
- Brief overview of the homework task and explanation of its sections.
- Description of the two tests to be conducted:
- Test if the average time in queue (TIQ) in the industry is 2.5 minutes or 150 seconds.
- Test for service time comparing PE with PT.
- Formulation of null and alternative hypotheses:
- Null hypothesis (H0): Average TIQ is greater than or equal to 150 seconds.
- Alternative hypothesis (H1): Average TIQ is less than 150 seconds.
- Criteria for choosing a z-test due to large sample size.
- Computation of critical value for the test using Excel formula
=NORM.S.INV(0.05).
- Steps to perform the z-test:
- Calculation of the average TIQ using Excel's
AVERAGEfunction. - Calculation of the standard deviation using Excel's
STDEVfunction. - Determining the number of observations.
- Computation of the z-statistics using the calculated values and the z-test formula.
- Calculation of the average TIQ using Excel's
- Hypothesis setting for the second test comparing service time of PT and PE:
- Null hypothesis (H0): Service time of PE is greater than or equal to PT.
- Alternative hypothesis (H1): Service time of PE is less than PT.
- Performing the same procedures as in the first test: selection of test (z-test due to large data set), calculation of critical value, and computation of z-statistics using the respective dataset.
- Explanation on how to make a decision based on the z-statistics: either to reject the null hypothesis or fail to reject it.
- Clarification on common mistakes made by students when interpreting the z-score (e.g., neglecting the direction of inequality).
- Discussion on the interpretation of test results and their implications for the business (e.g., if null hypothesis is true, what should the company do?).
- Explanation on how to write a report summarizing all the five steps of the hypothesis testing process.
- Emphasis on addressing all the required points in the assignment.
- Final advice and suggestions for students to perform these tests using their own datasets and interpret the results correctly.
- Encouragement to write a concise summary of the actions a company should take based on the test results.
- Appreciation for the students' hard work.
Throughout the module, there will be quizzes to test your knowledge on the topics we have covered. These quizzes will help you evaluate your understanding and identify areas where you may need to review.
During the virtual lecture, we will use active learning strategies to engage with the material and deepen our understanding. These strategies may include group discussions, problem-solving activities, and interactive simulations.
By the end of this module, you should have a strong foundation in AP Statistics and be well-prepared for the AP Statistics exam.