17 terms in 15
15.1: Hypothesis Test
A hypothesis test is a formal procedure for evaluating evidence against a null hypothesis H₀ using a test statistic and
Hypothesis Testing
15.1: Hypothesis Test
The null hypothesis H₀ is a statement that specifies no change, no effect, or no difference between groups. It represent
Hypothesis Testing
15.1: Hypothesis Test
The alternative hypothesis H₁ (or Hₐ) is a statement that contradicts the null hypothesis, typically asserting that an e
Hypothesis Testing
15.1: Hypothesis Test
The p-value is P(test statistic as extreme as observed | H₀ is true). For a two-sided test with test statistic z, p-valu
Hypothesis Testing
15.1: Hypothesis Test
The significance level α is the predetermined probability threshold for making a Type I error (rejecting a true null hyp
Hypothesis Testing
15.1: Hypothesis Test
A test statistic is a function of the sample data that follows a known distribution (such as t, z, or χ²) under the null
Hypothesis Testing
15.1: Hypothesis Test
A critical value is a point on the distribution of the test statistic that separates the rejection region from the non-r
Hypothesis Testing
15.1: Hypothesis Test
A confidence interval for parameter θ is an interval [L, U] calculated from sample data such that P(L < θ < U) = confide
Hypothesis Testing
15.1: Hypothesis Test
The t-distribution is a family of distributions indexed by degrees of freedom (df). For a sample of size n, df = n - 1.
Hypothesis Testing
15.1: Hypothesis Test
Degrees of freedom (df) is the number of independent pieces of information available for estimation or hypothesis testin
Hypothesis Testing
15.1: Hypothesis Test
A 95% confidence interval means that if sampling and interval calculation are repeated many times, about 95% of the calc
Hypothesis Testing
15.5: Type I Error
A Type I error occurs when you reject H₀ even though H₀ is true. The probability of making a Type I error is α (the sign
Hypothesis Testing
15.5: Type I Error
A Type II error occurs when you fail to reject H₀ even though H₀ is false. The probability of a Type II error is denoted
Hypothesis Testing
15.7: One-sided Test
In a one-sided (or one-tailed) test, the alternative hypothesis is directional: H₁: θ > θ₀ (right-tailed) or H₁: θ < θ₀
Hypothesis Testing
15.7: One-sided Test
In a two-sided (or two-tailed) test, the alternative hypothesis is non-directional: H₁: θ ≠ θ₀. The critical region is s
Hypothesis Testing