Skip to main content
Ch. 7 - Hypothesis Testing with One Sample
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Larson 8th EditionCh. 7 - Hypothesis Testing with One Sample문제 7.RE.3
7장, 문제 7.RE.3

n Exercises 1–6, the statement represents a claim. Write its complement and state which is H0 and which is Ha.


p < 0.205

검증된 단계별 안내
1
Identify the claim in the problem. The claim is 'p < 0.205', which is a statement about the population proportion (p).
Understand that the complement of the claim is the opposite of the inequality. The complement of 'p < 0.205' is 'p ≥ 0.205'.
Determine which statement represents the null hypothesis (H0) and which represents the alternative hypothesis (Ha). The null hypothesis (H0) always includes equality or '≥', while the alternative hypothesis (Ha) represents the claim or the inequality 'p < 0.205'.
Assign the hypotheses: H0: p ≥ 0.205 (the complement) and Ha: p < 0.205 (the claim).
Conclude that the null hypothesis (H0) is the statement to be tested, while the alternative hypothesis (Ha) is what we aim to support if the evidence is sufficient.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
2m
도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Null Hypothesis (H0)

The null hypothesis (H0) is a statement that indicates no effect or no difference, serving as a default position in statistical testing. In this context, it represents the claim that the population proportion is greater than or equal to 0.205, which is the opposite of the alternative hypothesis.
추천 영상:
06:21
Step 1: Write Hypotheses

Alternative Hypothesis (Ha)

The alternative hypothesis (Ha) is a statement that contradicts the null hypothesis, suggesting that there is an effect or a difference. For the given claim 'p < 0.205', the alternative hypothesis would be that the population proportion is indeed less than 0.205, indicating a specific direction of interest.
추천 영상:
06:21
Step 1: Write Hypotheses

Complement of a Statement

The complement of a statement refers to the opposite scenario of the original claim. In this case, the complement of 'p < 0.205' is 'p ≥ 0.205', which encompasses all values that are not less than 0.205, thus providing a complete view of the possible outcomes in hypothesis testing.
추천 영상:
4:23
Complementary Events
관련 실천
교과서 질문

n Exercises 1–6, the statement represents a claim. Write its complement and state which is H0 and which is Ha.


μ ≤ 375

35
views
교과서 질문

In Exercises 7–10, state the null and alternative hypotheses and identify which represents the claim,


An energy bar maker claims that the mean number of grams of carbohydrates in one bar is less than 25.

149
views
교과서 질문

In Exercises 29–34, find the critical value(s) and rejection region(s) for the type of t-test with level of significance α and sample size n.


Two-tailed test, α=0.02, n=12

97
views
교과서 질문

In Exercises 45–48, determine whether a normal sampling distribution can be used to approximate the binomial distribution. If it can, test the claim.


Claim: p≥0.04; α=0.10

Sample statistics: p_hat = 0.03, n=30

56
views
교과서 질문

In Exercises 29–34, find the critical value(s) and rejection region(s) for the type of t-test with level of significance α and sample size n.


Left-tailed test, α=0.05, n=15

77
views
교과서 질문

In Exercises 55–58, test the claim about the population variance or standard deviation at the level of significance . Assume the population is normally distributed.


Claim: σ^2 > 2; α=0.10. Sample statistics: s^2 = 2.95, n=18

72
views