Podcast
Questions and Answers
What is the mistake made in a Type I error during hypothesis testing?
What is the mistake made in a Type I error during hypothesis testing?
- Failing to reject the null hypothesis when it is false
- Not conducting a hypothesis test
- Rejecting the null hypothesis when it is true (correct)
- Accepting the null hypothesis when it should be rejected
Which symbol represents the probability of committing a Type I error?
Which symbol represents the probability of committing a Type I error?
- α (correct)
- δ
- β
- θ
In hypothesis testing, what should be the nature of the significance level α when the consequences of a Type I error are serious?
In hypothesis testing, what should be the nature of the significance level α when the consequences of a Type I error are serious?
- It should be set to 1
- It should be made larger
- It should be made smaller (correct)
- It should be set to 0.5
What is the correct action if the P-value obtained is greater than the significance level α?
What is the correct action if the P-value obtained is greater than the significance level α?
Which of the following is NOT a step in the P-value method of hypothesis testing?
Which of the following is NOT a step in the P-value method of hypothesis testing?
Which hypothesis represents what the researcher is trying to prove?
Which hypothesis represents what the researcher is trying to prove?
What should be avoided in the conclusion of a hypothesis test?
What should be avoided in the conclusion of a hypothesis test?
Which error occurs when the null hypothesis is falsely accepted?
Which error occurs when the null hypothesis is falsely accepted?
What does the null hypothesis (H0) represent in hypothesis testing?
What does the null hypothesis (H0) represent in hypothesis testing?
Which of the following is true about hypothesis tests?
Which of the following is true about hypothesis tests?
In hypothesis testing, what is the purpose of calculating the test statistic?
In hypothesis testing, what is the purpose of calculating the test statistic?
How is the alternative hypothesis typically represented?
How is the alternative hypothesis typically represented?
What is the P-value in hypothesis testing?
What is the P-value in hypothesis testing?
Which of the following statements is a characteristic of an alternative hypothesis?
Which of the following statements is a characteristic of an alternative hypothesis?
What should be stated as the conclusion of a hypothesis test?
What should be stated as the conclusion of a hypothesis test?
What is a major purpose of hypothesis testing?
What is a major purpose of hypothesis testing?
What is the primary purpose of the null hypothesis (H0) in hypothesis testing?
What is the primary purpose of the null hypothesis (H0) in hypothesis testing?
Which of the following correctly represents the alternative hypothesis when the parameter is claimed to be less than a certain value?
Which of the following correctly represents the alternative hypothesis when the parameter is claimed to be less than a certain value?
When stating hypotheses, which of the following symbols is typically used for the null hypothesis?
When stating hypotheses, which of the following symbols is typically used for the null hypothesis?
In testing the claim that the mean of a population equals 100, what would the null hypothesis (H0) be?
In testing the claim that the mean of a population equals 100, what would the null hypothesis (H0) be?
What does the critical region in hypothesis testing represent?
What does the critical region in hypothesis testing represent?
What must be true for the alternative hypothesis (H1) when H0 claims a parameter is equal to a specific value?
What must be true for the alternative hypothesis (H1) when H0 claims a parameter is equal to a specific value?
If the null hypothesis states H0: µ = 195 lb, what would be the appropriate statement for H1 if the claim is that the mean is more than 195 lb?
If the null hypothesis states H0: µ = 195 lb, what would be the appropriate statement for H1 if the claim is that the mean is more than 195 lb?
Which of the following is NOT typically true about the null hypothesis in statistical testing?
Which of the following is NOT typically true about the null hypothesis in statistical testing?
Flashcards
Null Hypothesis (H0)
Null Hypothesis (H0)
A claim about a population parameter that is being tested in a hypothesis test.
Alternative Hypothesis (Ha)
Alternative Hypothesis (Ha)
A hypothesis that contradicts the null hypothesis and is accepted if the null hypothesis is rejected.
Hypothesis Test
Hypothesis Test
A procedure for testing a claim about a property of a population.
Test Statistic
Test Statistic
Signup and view all the flashcards
P-value
P-value
Signup and view all the flashcards
Critical Value(s)
Critical Value(s)
Signup and view all the flashcards
Conclusion of a Hypothesis Test
Conclusion of a Hypothesis Test
Signup and view all the flashcards
Non-Technical Conclusion
Non-Technical Conclusion
Signup and view all the flashcards
Critical Region
Critical Region
Signup and view all the flashcards
Significance Level (α)
Significance Level (α)
Signup and view all the flashcards
Test of Significance
Test of Significance
Signup and view all the flashcards
Type 1 Error
Type 1 Error
Signup and view all the flashcards
Type II Error
Type II Error
Signup and view all the flashcards
Traditional Method
Traditional Method
Signup and view all the flashcards
Study Notes
Hypothesis Testing
- Hypothesis testing is a procedure for deciding between two competing claims about a population parameter.
- The null hypothesis (H₀) is the claim being tested, often stating equality.
- The alternative hypothesis (H₁) is the claim we consider if the null hypothesis is false. It often states an inequality (≠, <, >).
- The significance level (α) represents the probability of rejecting the null hypothesis when it's true. Common values are 0.05, 0.01, and 0.10.
- A critical region (or rejection region) contains values of the test statistic that lead to rejecting the null hypothesis.
- A test statistic is a value calculated from sample data to assess the validity of the null hypothesis.
- A critical value separates the critical region from the values that do not lead to rejection of the null hypothesis.
- Hypothesis tests can be two-tailed (both tails of the distribution are considered), left-tailed (only the left tail), or right-tailed (only the right tail).
- The p-value is the probability of obtaining a sample statistic as extreme as, or more extreme than, the one observed, assuming the null hypothesis is true. If the p-value is less than or equal to the significance level (α), the null hypothesis is rejected.
Types of Hypothesis Tests
-
Two-tailed: The alternative hypothesis states that the parameter is not equal to a specific value(H₁: ≠).
-
Left-tailed: The alternative hypothesis states that the parameter is less than a specific value (H₁: <). The critical region is situated in the left tail of the distribution.
-
Right-tailed: The alternative hypothesis states that the parameter is greater than a specific value (H₁: >). The critical region is situated in the right tail of the distribution.
Errors in Hypothesis Tests
- Type I Error: Rejecting the null hypothesis when it's actually true. (Probability = α)
- Type II Error: Failing to reject the null hypothesis when it's actually false. (Probability = β)
Confidence Method for Hypothesis Testing
- Constructing a confidence interval (CI) is an alternative approach.
- If the claimed value for the parameter is not contained within the confidence interval, then we can reject the claim.
- For one-tailed tests, we construct a confidence interval with level 1-2α.
Testing Claims About a Mean: σ Known
- Requirements:
- Simple random sample.
- Population standard deviation (σ) known.
- Either or both of these conditions are satisfied:
- Population is normally distributed.
- Sample size (n) is greater than or equal to 30 (n ≥ 30).
Testing Claims About a Mean: σ Not Known
- Requirements:
- Simple random sample.
- Population standard deviation (σ) unknown.
- Either or both of these conditions are satisfied:
- Population is normally distributed.
- Sample size (n) is greater than or equal to 30 (n ≥ 30).
- Use the t-distribution for calculations. The degrees of freedom are (n-1).
P-Values and the Student t-Distribution
- The t-distribution table doesn’t give exact p-values. Use the tables to identify a range of possible p-values.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
