Math Problem Statement
Solution
In this question, you're asked to determine what type of hypothesis test is being performed based on the given null and alternative hypotheses:
- Null Hypothesis ():
- Alternative Hypothesis ():
Explanation:
- The null hypothesis () is a statement of no effect or no difference, which is .
- The alternative hypothesis () suggests that the population proportion is less than 0.43.
Since the alternative hypothesis uses a "less than" () symbol, this indicates that you are testing whether the parameter is less than a certain value. Therefore, this is a left-tailed test because you're only concerned with the lower side of the distribution.
Answer:
The correct option is left-tailed.
Would you like more details on hypothesis testing? Here are some related questions you might find useful:
- What is the difference between one-tailed and two-tailed tests?
- How do you interpret p-values in hypothesis tests?
- When should you use a left-tailed vs. right-tailed test?
- How does the significance level () affect hypothesis testing?
- What are Type I and Type II errors in hypothesis testing?
Tip: For left-tailed tests, the critical region is on the left side of the distribution, where you expect values smaller than the hypothesized parameter value.
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Math Problem Analysis
Mathematical Concepts
Hypothesis Testing
Null Hypothesis
Alternative Hypothesis
Proportion Testing
Formulas
-
Theorems
One-Tailed Hypothesis Testing
Suitable Grade Level
Grades 11-12 or introductory college level
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