8.7: Chapter 8 Key Terms and Symbols
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Glossary of Key Terms and Symbols
Key Terms
Alternative Hypothesis (H₁): The statement that there is an effect or a difference; it is the logical complement of H₀.
Confidence Level (1 − α): The probability that the confidence interval contains the true population parameter.
Critical Value Method: A traditional approach where the test statistic is compared to a cutoff value from the z or t distribution.
Hypothesis Testing: A method for making decisions about population parameters using sample data.
Null Hypothesis (H₀): The assumption that there is no effect or no difference. It is assumed true until evidence suggests otherwise.
One-Sample t-Test for the Mean: Used when the population standard deviation is unknown and the sample is drawn from a normally distributed population.
One-Sample z-Test for a Proportion: Used to test a claim about a population proportion when the sample size is large enough to satisfy normal approximation conditions.
One-Sample z-Test for the Mean: Used when the population standard deviation is known and the sample size is large or the population is normally distributed.
Parameter: A numerical measure that describes a characteristic of a population (e.g., population mean or proportion).
p-Value Method: A modern approach that calculates the probability of the observed sample result under H₀. If the p-value is less than α, H₀ is rejected.
Significance Level (α): The probability of making a Type I Error, or rejecting H₀ when it is true. Common values are 0.05 or 0.01.
Statistic: A numerical measure that describes a characteristic of a sample, used to estimate a population parameter.
Statistical Hypothesis: A claim or conjecture about a population parameter that can be tested with sample data.
Test Statistic: A standardized value (z or t) used to decide whether to reject H₀. It compares the sample result to the expected result under H₀.
Type I Error (α): Rejecting H₀ when H₀ is true.
Type II Error (β): Failing to reject H₀ when H₀ is false.
Key Symbols
\( H_0 \) - Null hypothesis.
\( H_1 \) - Alternative hypothesis.
\( \alpha \) - Significance level (probability of a Type I error).
\( \beta \) - Probability of a Type II error.
\( \bar{x} \) - Sample mean.
\( \mu \) - Population mean.
\( p \) - Population proportion.
\( \hat{p} \) - Sample proportion.
\( n \) - Sample size.
\( \sigma \) - Population standard deviation.
\( s \) - Sample standard deviation.
\( z \) - Test statistic for z-tests (when population standard deviation is known).
\( t \) - Test statistic for t-tests (when population standard deviation is unknown).
\( z_{\alpha/2} \) - Critical z-value for two-tailed tests.
\( t_{\alpha/2} \) - Critical t-value for two-tailed tests.
p-value - Probability of observing the test result under the assumption that \( H_0 \) is true.
SE - Standard error (standard deviation of the sampling distribution).
Authors
"8.7: Chapter 8 Key Terms and Symbols" by Toros Berberyan, Tracy Nguyen, and Alfie Swan is licensed under CC BY 4.0