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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?
Which symbol represents the probability of committing a Type I error?
Which symbol represents the probability of committing a Type I error?
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?
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?
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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?
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Which hypothesis represents what the researcher is trying to prove?
Which hypothesis represents what the researcher is trying to prove?
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What should be avoided in the conclusion of a hypothesis test?
What should be avoided in the conclusion of a hypothesis test?
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Which error occurs when the null hypothesis is falsely accepted?
Which error occurs when the null hypothesis is falsely accepted?
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What does the null hypothesis (H0) represent in hypothesis testing?
What does the null hypothesis (H0) represent in hypothesis testing?
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Which of the following is true about hypothesis tests?
Which of the following is true about hypothesis tests?
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In hypothesis testing, what is the purpose of calculating the test statistic?
In hypothesis testing, what is the purpose of calculating the test statistic?
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How is the alternative hypothesis typically represented?
How is the alternative hypothesis typically represented?
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What is the P-value in hypothesis testing?
What is the P-value in hypothesis testing?
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Which of the following statements is a characteristic of an alternative hypothesis?
Which of the following statements is a characteristic of an alternative hypothesis?
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What should be stated as the conclusion of a hypothesis test?
What should be stated as the conclusion of a hypothesis test?
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What is a major purpose of hypothesis testing?
What is a major purpose of hypothesis testing?
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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?
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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?
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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?
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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?
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What does the critical region in hypothesis testing represent?
What does the critical region in hypothesis testing represent?
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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?
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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?
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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?
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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
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Two-tailed: The alternative hypothesis states that the parameter is not equal to a specific value(H₁: ≠).
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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.
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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.
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Description
This quiz covers the essential concepts of hypothesis testing, including null and alternative hypotheses, significance levels, and critical regions. Test your understanding of these fundamental statistical principles and their applications in decision-making.
