Math Problem Statement

What is the p value

Solution

To find the p-value for the test statistic z0.9317z \approx -0.9317, we need to use the standard normal distribution table (or a computational tool). The p-value corresponds to the probability of observing a test statistic as extreme as, or more extreme than, the one observed under the null hypothesis.

Since we are dealing with a two-tailed test (we are interested in deviations in both directions), the p-value is:

p-value=2×P(Z0.9317)\text{p-value} = 2 \times P(Z \leq -0.9317)

First, we find the probability P(Z0.9317)P(Z \leq -0.9317) using the standard normal distribution table or a calculator.

Using a standard normal distribution table or a calculator, we find:

P(Z0.9317)0.1763P(Z \leq -0.9317) \approx 0.1763

So, the p-value is:

p-value=2×0.1763=0.3526\text{p-value} = 2 \times 0.1763 = 0.3526

Therefore, the p-value is approximately 0.3526.

Would you like more details or have any questions about this calculation?

Here are 8 related questions to expand on this information:

  1. What is the significance level typically used in hypothesis testing, and how does it relate to the p-value?
  2. How would you interpret the p-value in the context of this study?
  3. What conclusions can be drawn if the p-value is less than the significance level?
  4. How can the p-value help in understanding the effectiveness of the drug in preventing heart attacks?
  5. What are the limitations of using the p-value in hypothesis testing?
  6. How would you explain the concept of a p-value to someone with no statistical background?
  7. What other statistical tests can be used for comparing proportions?
  8. How can the sample size affect the p-value and the power of the test?

Tip: When interpreting p-values, it is essential to consider the context of the study and the chosen significance level. A high p-value suggests that the observed data is consistent with the null hypothesis, while a low p-value indicates that the observed data is unlikely under the null hypothesis.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
Standard Normal Distribution
Two-Tailed Test

Formulas

P-value calculation: p-value = 2 * P(Z <= z)

Theorems

-

Suitable Grade Level

Advanced Undergraduate