Stat 201 UTK Final Exam Flashcards

Questions and Answers

Which of the following must be met for all confidence intervals?

Less than 10% Condition (correct)

Randomness (correct)

Normal Distribution

Independent Means

When do you use the Success/Failure for the 3rd condition?

Categorical Variables

What condition do you need 5 of?

Expected Cell Count

When doing the hypothesis test on the mean, which is a condition that must be met?

Nearly Normal Condition Signup and view all the answers

What must be met for all quantitative data (means) tests and intervals?

Nearly Normal Signup and view all the answers

What must be met for the chi-square test of independence?

Count Data and Expected Cell Count Signup and view all the answers

On JMP what do you look at to determine the p-value?

Look at Prob>ChiSq Signup and view all the answers

What is the smallest Chi-Square value you can get?

ZERO ChiSq cannot go below zero Signup and view all the answers

What is the relationship regarding Chi-Square and the P-value?

Bigger the Chi-Square the smaller the p-value Signup and view all the answers

When the p-value is lower than the alpha (0.05)...

We reject the Null Signup and view all the answers

When the p-value is higher than the alpha (0.05)...

We fail to reject the Null Signup and view all the answers

If we reject the null we...

Have Evidence Signup and view all the answers

If we fail to reject the null we....

Do not Have Evidence Signup and view all the answers

If the p-value is high we...

Let it fly Signup and view all the answers

What is a Type 1 error?

The null is true but we reject it Signup and view all the answers

What is a Type 2 error?

The null is false and we fail to reject it Signup and view all the answers

What is an example of a Type 2 Error?

You leave the tree up and it falls Signup and view all the answers

What is an example of a Type 1 Error?

You think it is a snake but it is not Signup and view all the answers

What are the three things that control power?

Sample Size, Alpha, Effect Size Signup and view all the answers

What is the equation to find Power?

Power = 1-Beta Signup and view all the answers

To test the mean we use a sample size of 98, a standard deviation of 2 and a mean of 3. Find the Degrees of Freedom.

97 Signup and view all the answers

How do you find the Degrees of Freedom for a one-sample-t?

Use N-1 Signup and view all the answers

How do you find the Degrees of Freedom for a two-sample-t?

It's complicated Signup and view all the answers

How do you find the Degrees of Freedom for a Chi-squared?

(rows-1)(columns-1) Signup and view all the answers

What are the three conditions for the confidence interval for the difference between two means?

Independent Means, Nearly Normal, and Success/Failure Signup and view all the answers

When doing the two-sample T-test the variables will be...

Category/Quantity Signup and view all the answers

What are some ways to check for the nearly normal condition?

Normal Probability Plot, Histogram, Goodness of Fit test Signup and view all the answers

What is not a way to check for the nearly normal condition?

Degrees of freedom > 10 Signup and view all the answers

A researcher wants to examine the true GPA of students at UTK. What type of test will they use?

A One Sample T-Test Signup and view all the answers

To examine the differences between GPAs of students and if they own a dog, what type of test will they use?

A Two Sample T-Test Signup and view all the answers

While attending UT, people find a favorite place to eat? Favorite restaurant vs. year at UT? What test would we use?

Chi-Squared Test Signup and view all the answers

What is NOT an example of a valid alternative hypothesis?

p=0.36 Signup and view all the answers

What is an example of a valid alternative hypothesis?

p=/=0.36, p>0.36, p<0.36 Signup and view all the answers

Study Notes

Confidence Intervals

Must satisfy randomness and the less than 10% condition.
For categorical variables, utilize the success/failure condition.

Chi-Square Tests

Require count data and expected cell counts.
To assess p-value in JMP, check Prob>ChiSq.
The smallest Chi-Square value achievable is zero.

Hypothesis Testing

Conduct hypothesis test on the mean requires the nearly normal condition.
For all quantitative data (means) tests and intervals, the nearly normal condition is necessary.
When the p-value is below alpha (0.05), reject the null hypothesis, indicating evidence.
If the p-value is above alpha, fail to reject the null, signifying lack of evidence.
A high p-value suggests to "let it fly."

Types of Errors

Type 1 error occurs when the null hypothesis is true, but it is rejected.
Type 2 error happens when the null hypothesis is false, yet it is not rejected.
Practical examples: Type 1 - mistakenly identifying a harmless object as dangerous; Type 2 - not removing a potentially hazardous tree that eventually falls.

Power of a Test

Power is influenced by sample size, alpha level, and effect size.
Equation for power calculation: Power = 1 - Beta.

Degrees of Freedom

For one-sample t-test: calculated as N - 1.
For two-sample t-test: determination is complex.
For Chi-squared test: calculated with the formula (rows - 1)(columns - 1).

Two-Sample T-Test

Conditions for confidence interval: independent means, nearly normal distribution, and success/failure condition should be fulfilled.
Tests involve comparing categorical and quantitative variables.

Normality Check

Checking nearly normal condition can be done through Normal Probability Plots, histograms, and goodness of fit tests.
A common misconception is that having degrees of freedom greater than 10 ensures normality.

Specific Tests for GPA

One Sample T-Test is appropriate for examining true GPA of students.
A Two Sample T-Test is suitable for comparing GPAs between students with and without dogs.
Chi-Squared Test is utilized for associations (e.g., favorite restaurant vs. year at UT).

Alternative Hypotheses

Valid examples include p ≠ 0.36, p > 0.36, or estimations involving p.
Invalid alternative hypotheses would state specific probabilities like p = 0.36.

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Test your knowledge in statistics with these flashcards designed for the Stat 201 UTK Final Exam. Cover essential concepts such as confidence intervals, conditions for hypothesis testing, and more. Ideal for students looking to review key statistical principles before the exam.