Math Problem Statement

You are performing a two-tailed test with test statistic z = -2.86, find the p-value to 4 decimal places.

Solution

To find the p-value for a two-tailed test with a given zz-score of z=2.86z = -2.86:

  1. First, find the probability associated with z=2.86z = -2.86 on a standard normal distribution (this is the area to the left of z=2.86z = -2.86).

  2. For z=2.86z = -2.86, the left-tail probability is approximately 0.0021.

  3. Since this is a two-tailed test, we double this probability: p-value=2×0.0021=0.0042p\text{-value} = 2 \times 0.0021 = 0.0042

Answer: The p-value to four decimal places is 0.00420.0042.

Would you like a detailed explanation of each step, or do you have any questions?


Here are 5 related questions for further exploration:

  1. How would the p-value change if this were a one-tailed test instead?
  2. What does a p-value of 0.0042 imply about the null hypothesis in a hypothesis test?
  3. How do you interpret a negative zz-score in the context of hypothesis testing?
  4. How does changing the significance level affect the conclusions drawn from this p-value?
  5. Can you calculate the p-value if the zz-score were 2.862.86 (positive) instead?

Tip: In two-tailed tests, always remember to double the tail probability to get the p-value.

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Math Problem Analysis

Mathematical Concepts

Statistics
Hypothesis Testing
Standard Normal Distribution
Two-Tailed Test

Formulas

P-value for a two-tailed test: p = 2 * P(Z < z)

Theorems

Properties of the Standard Normal Distribution

Suitable Grade Level

Grades 11-12