Math Problem Statement
H0: m=4 versus H1: m≠4. Since the 95% confidence interval (Blank: A. contains, B. does not contain) m0, then H0 (Blank: A. will, B. will not) be rejected at the 0.05 level.
Solution
To answer this question:
Key Points to Consider:
-
Hypotheses:
- Null Hypothesis ():
- Alternative Hypothesis ():
-
Confidence Interval Relationship:
- The 95% confidence interval reflects a range of plausible values for the population mean () based on sample data.
- If the hypothesized value () lies inside the confidence interval, we fail to reject .
- If the hypothesized value () lies outside the confidence interval, we reject .
-
Significance Level:
- At a level, a 95% confidence interval corresponds directly to the hypothesis test.
Completing the Sentence:
-
If the confidence interval contains :
- Select A. contains.
- Then, will not be rejected at the level (select B. will not).
-
If the confidence interval does not contain :
- Select B. does not contain.
- Then, will be rejected at the level (select A. will).
Final Selection Based on Confidence Interval:
- If you determine the confidence interval relative to , substitute the appropriate answers into the blanks.
Would you like additional clarification or details? Let me know! Here are related questions to expand your understanding:
- What is the relationship between confidence intervals and p-values in hypothesis testing?
- How do we calculate a confidence interval for a given dataset?
- What does it mean to set a two-tailed hypothesis test, as in this example?
- How does the confidence level (e.g., 95%) influence the hypothesis test decision?
- Can a result be significant at a lower confidence level but not at 95%?
Tip: Always visualize the confidence interval on a number line to check if the hypothesized value falls within or outside the range.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Hypothesis Testing
Confidence Intervals
Significance Levels
Formulas
Confidence interval formula
Relationship between confidence intervals and hypothesis testing
Theorems
Central Limit Theorem
Concept of p-value in hypothesis testing
Suitable Grade Level
Undergraduate (Statistics or Data Analysis Courses)
Related Recommendation
Understanding Hypothesis Testing with a 55% Significance Level
Relationship Between Confidence Intervals and Hypothesis Testing
Hypothesis Testing with Confidence Intervals at 95% Level
Determining Normal Confidence Intervals for c = 0.95 and c = 0.98
Hypothesis Testing: Rejecting the Null Hypothesis H0 at Alpha = 0.05