Textbook Question
True or False? In Exercises 5–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.
A large P-value in a test will favor rejection of the null hypothesis.
14
views
9. Hypothesis Testing for One Sample
Steps in Hypothesis Testing
1:47 minutesProblem 7.1.16
Textbook Question
Stating Hypotheses In Exercises 11–16, the statement represents a claim. Write its complement and state which is H0 and which is Ha.
p = 0.21
Verified step by step guidance1
Identify the claim in the problem. The claim is that the population proportion is equal to 0.21, which can be written as p = 0.21.
Write the complement of the claim. The complement of 'p = 0.21' is 'p ≠ 0.21', as the complement represents all values not equal to 0.21.
Determine which statement is the null hypothesis (H₀). The null hypothesis always includes equality, so H₀: p = 0.21.
Determine which statement is the alternative hypothesis (Hₐ). The alternative hypothesis is the complement of the null hypothesis, so Hₐ: p ≠ 0.21.
Summarize the hypotheses: H₀: p = 0.21 (the claim) and Hₐ: p ≠ 0.21 (the complement).
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
1mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Hypothesis Testing
Hypothesis testing is a statistical method used to make decisions about a population based on sample data. It involves formulating two competing hypotheses: the null hypothesis (H0), which represents a statement of no effect or no difference, and the alternative hypothesis (Ha), which represents the claim being tested. The goal is to determine whether there is enough evidence to reject H0 in favor of Ha.
Recommended video:
Guided course
06:21
Step 1: Write Hypotheses
Null and Alternative Hypotheses
The null hypothesis (H0) is a statement that indicates no change or no effect, serving as a default position that there is no relationship between variables. The alternative hypothesis (Ha) is the statement that reflects the claim or effect that the researcher aims to support. In the context of the given question, H0 would state that the population proportion p is equal to 0.21, while Ha would state that p is not equal to 0.21.
Recommended video:
Guided course
06:21Step 1: Write Hypotheses
Complement of a Hypothesis
The complement of a hypothesis refers to the opposite of the original statement. In hypothesis testing, if the null hypothesis states a specific value (e.g., p = 0.21), the complement would encompass all other possibilities (e.g., p ≠ 0.21). Understanding the complement is crucial for correctly formulating the alternative hypothesis and interpreting the results of the hypothesis test.
Recommended video:
4:23Complementary Events
6:21mWatch next
Master Step 1: Write Hypotheses with a bite sized video explanation from Patrick
Start learningRelated Videos
Related Practice