Math Problem Statement
what is the P-value ? dont round answer
Solution
To calculate the p-value, we need to use the provided test statistic . Since the problem states that we are using a significance level of 0.01 and testing the difference between two means ( and ), we'll find the p-value for a two-tailed test because the hypotheses are:
- Null hypothesis ():
- Alternative hypothesis ():
Given the test statistic , we need to find the p-value using the t-distribution. The degrees of freedom can be approximated using the formula for unequal variances, but since the exact values are not given, we'll approximate it assuming a large sample size, which typically allows us to use the normal approximation.
Calculation:
- The test is two-tailed, so we calculate the p-value as .
Using a t-table or statistical software for the t-distribution:
Assuming a large degrees of freedom (close to normal distribution), the p-value would be approximately calculated using the normal distribution.
Let's compute it numerically:
So the p-value:
The p-value is approximately 0.148 when not rounded.
Would you like further explanation or assistance with another related concept?
Related Questions:
- How do you determine whether to use a one-tailed or two-tailed test?
- What are the assumptions behind using a t-test?
- How does sample size affect the degrees of freedom and test results?
- What does the p-value tell us about the statistical significance of the test?
- How would the result change if a different significance level was used?
Tip:
Always verify assumptions such as normality and equal variances before conducting a t-test, as these impact the validity of your results.
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Math Problem Analysis
Mathematical Concepts
Hypothesis Testing
T-Distribution
P-Value Calculation
Two-Sample T-Test
Formulas
P(T > t) = p-value
P-value for two-tailed test = 2 × P(T > test statistic)
Theorems
T-Test Theorem for Two Independent Means
Central Limit Theorem (for normal distribution approximation)
Suitable Grade Level
Grades 11-12 (Advanced Statistics) / Undergraduate Level
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