Math Problem Statement
What is the p value
Solution
To find the p-value for the test statistic , 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:
First, we find the probability using the standard normal distribution table or a calculator.
Using a standard normal distribution table or a calculator, we find:
So, the p-value is:
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:
- What is the significance level typically used in hypothesis testing, and how does it relate to the p-value?
- How would you interpret the p-value in the context of this study?
- What conclusions can be drawn if the p-value is less than the significance level?
- How can the p-value help in understanding the effectiveness of the drug in preventing heart attacks?
- What are the limitations of using the p-value in hypothesis testing?
- How would you explain the concept of a p-value to someone with no statistical background?
- What other statistical tests can be used for comparing proportions?
- 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.
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Math Problem Analysis
Mathematical Concepts
Hypothesis Testing
Standard Normal Distribution
Two-Tailed Test
Formulas
P-value calculation: p-value = 2 * P(Z <= z)
Theorems
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Suitable Grade Level
Advanced Undergraduate
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