STAT 200 Learning Objectives

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Questions and Answers

What effect does increasing the sample size have on the width of a confidence interval?

It decreases the width of the confidence interval. (correct)

It can either increase or decrease the width depending on the standard error.

It increases the width of the confidence interval.

It has no effect on the width of the confidence interval.

In hypothesis testing, what is a correct definition of a p-value?

The probability of making a type-1 error.

The probability of observing data as extreme as observed, given that the null hypothesis is true. (correct)

The probability of the null hypothesis being true.

The threshold at which the null hypothesis is rejected.

What would correctly constitute a null hypothesis when testing for the difference in means between two groups?

At least one group has a significantly different mean.

The means of the two groups are equal. (correct)

The means of the two groups are not equal.

The means of both groups are assumed to be greater than a specific value.

When using a bootstrap distribution to construct confidence intervals, what calculation is commonly applied?

The statistic ± 2 times the standard error. Signup and view all the answers

In the context of hypothesis testing, what is a type-2 error?

Failing to reject a false null hypothesis. Signup and view all the answers

What is the main difference between a population and a sample?

A population is the entire group being studied, while a sample is a subset of that group. Signup and view all the answers

Which variable in a regression analysis describes the variable that is being predicted?

Response variable Signup and view all the answers

In hypothesis testing for two categorical variables, which of the following steps is NOT required?

Using regression analysis to find slope Signup and view all the answers

What does the R-squared value in regression analysis represent?

The proportion of variance explained by the independent variable Signup and view all the answers

What type of variable is a confounding variable?

A variable that affects both the explanatory and the response variable Signup and view all the answers

Which of the following describes the concept of standard error?

The average distance that a sample statistic is from the population parameter Signup and view all the answers

In the context of linear regression, what does the slope indicate?

The change in the response variable for a one-unit change in the explanatory variable Signup and view all the answers

What type of relationship does correlation measure between two variables?

Strength and direction of a linear relationship Signup and view all the answers

Study Notes

STAT 200 Learning Objectives

Variables: Explain, recognize, and provide examples of categorical and quantitative variables.
Numerical Summaries: Interpret numerical summaries of center/location (e.g., five-number summaries) and spread (e.g., empirical rule); predict how data changes affect these summaries.
Graphical Displays: Derive information from univariate and bivariate graphical displays (bar graphs, dot-plots, boxplots, histograms, scatterplots).
Probabilities and Z-scores: Convert values to percentiles or z-scores for normal distributions using technology.
Linear Regression: Identify and interpret slope, intercept, R-squared values from simple linear regression output; calculate predicted values and residuals. Interpret T-statistic and p-value for the test of slope coefficients.
Correlation and Bivariate Plots: Match bivariate plots and descriptions to correlation coefficients; calculate correlation from R-squared and slope.
Descriptive Statistics: Produce and interpret descriptive statistics for tabular data (conditional probabilities, risk, relative risk, odds). Include hypothesis tests for two categorical variables.
Hypothesis Tests: Perform steps in a hypothesis test of association of two categorical variables from contingency table data; formulate hypotheses, calculate expected counts, find the chi-square statistic, calculate p-value, and interpret results.
Population vs. Sample: Recognize the difference between population and sample, and between parameter and statistic.
Sample Size and Standard Error: For large populations, understand that precision of estimation is a function of sample size. Recognize the inverse square root relationship between sample size and standard error.
Study Types: Recognize randomized experiment vs. observational study and explain implications for causation; define simple random sampling.
Variables in Studies: Explain, recognize, and cite examples of explanatory, response, and confounding (lurking) variables.
Confidence Intervals: Recognize the similarity among confidence intervals; exploit this similarity to derive intervals for common population quantities (proportions and means).
Confidence Interval Details: Give correct informal and formal explanations of confidence intervals; explain how factors like sample size, confidence level, and standard error affect the interval's width.
Hypothesis Formulation: Correctly construct null and alternative hypotheses about population quantities in real-life situations.
Test Statistics and P-values: Recognize similarity among test statistics of the standardized score variety (e.g., proportions, means); calculate p-values, define p-value correctly, and interpret p-values and confidence intervals for decision-making.
Inference Situations: Recognize and distinguish among common inference situations (one mean/proportion, difference of two means/proportions, paired means), apply and interpret confidence intervals and tests in these situations.
Bootstrap Distributions: Explain how to generate and use a bootstrap distribution to create confidence intervals for means, differences in means, proportions, and differences in proportions; use both formula (statistic ± 2xSE) and percentiles.
Randomization Distributions: Describe the process of creating a randomization distribution for a given sample and null hypothesis; use technology to calculate p-value, connecting it to the motivation behind a randomization distribution.

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Description

This quiz covers key learning objectives for STAT 200, including variables, numerical summaries, graphical displays, probabilities, linear regression, and correlation. Students will be tested on their understanding of these foundational concepts in statistics. Prepare to apply theoretical knowledge with practical examples and calculations.