Math Problem Statement

What are the two types of hypotheses used in a hypothesis​ test? How are they​ related?

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Part 1

What are the two types of hypotheses used in a hypothesis​ test?

null and alternative

​left-tailed and​ right-tailed

population and sample

type I and type II

Solution

The two types of hypotheses used in a hypothesis test are the null hypothesis and the alternative hypothesis.

Explanation:

  1. Null Hypothesis (H₀):

    • It is a statement that assumes no effect, no difference, or no change. It is the hypothesis that researchers seek to test against. The null hypothesis is typically stated as an equality (e.g., H0:μ=5H_0: \mu = 5), implying that any observed differences in the data are due to random chance.
  2. Alternative Hypothesis (H₁ or Hₐ):

    • This hypothesis contradicts the null hypothesis. It suggests that there is an effect, a difference, or a change. The alternative hypothesis is usually expressed as an inequality (e.g., H1:μ5H_1: \mu \neq 5, H1:μ>5H_1: \mu > 5, or H1:μ<5H_1: \mu < 5).

Relationship Between the Two:

  • The null and alternative hypotheses are complementary; they cover all possible outcomes of the test. If the data provides sufficient evidence, the null hypothesis is rejected in favor of the alternative hypothesis. Otherwise, the null hypothesis is not rejected.

Answer Choice:

  • The correct choice is "null and alternative."

Would you like more details or have any questions?

Related Questions:

  1. What is the role of the p-value in hypothesis testing?
  2. How do you determine if a hypothesis test is left-tailed, right-tailed, or two-tailed?
  3. What are Type I and Type II errors in hypothesis testing?
  4. How do you interpret the results if the null hypothesis is not rejected?
  5. What are the steps involved in conducting a hypothesis test?

Tip:

Always state the null and alternative hypotheses clearly before performing any calculations in hypothesis testing.

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Math Problem Analysis

Mathematical Concepts

Statistics
Hypothesis Testing

Formulas

None (conceptual explanation focused on null and alternative hypotheses)

Theorems

Null Hypothesis (H₀)
Alternative Hypothesis (H₁ or Hₐ)

Suitable Grade Level

Grades 11-12