Math Problem Statement

If the null and alternative hypotheses are: H0: p = 0.43, H1: p < 0.43, what kind of test is this?

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 (H0H_0): p=0.43p = 0.43
  • Alternative Hypothesis (H1H_1): p<0.43p < 0.43

Explanation:

  • The null hypothesis (H0H_0) is a statement of no effect or no difference, which is p=0.43p = 0.43.
  • The alternative hypothesis (H1H_1) suggests that the population proportion pp 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:

  1. What is the difference between one-tailed and two-tailed tests?
  2. How do you interpret p-values in hypothesis tests?
  3. When should you use a left-tailed vs. right-tailed test?
  4. How does the significance level (α\alpha) affect hypothesis testing?
  5. 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