Question 1177044: 12.) Find the P-value for the following values of the test statistic t, sample size n, and alternate hypothesis H1. If you use Table A.3, you may specify that P is between two values.
d.t = 3.635, n = 4, H1: μ > μ0
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's find the P-value for the given t-statistic, sample size, and alternate hypothesis.
**Understanding the Problem**
* **t-statistic (t):** 3.635
* **Sample size (n):** 4
* **Alternate hypothesis (H1):** μ > μ0 (right-tailed test)
**Steps to Calculate the P-value**
1. **Calculate the Degrees of Freedom (df):**
df = n - 1 = 4 - 1 = 3
2. **Use the t-distribution:**
We need to find the probability that a t-distributed random variable with 3 degrees of freedom is greater than 3.635.
3. **Use a t-table or calculator/software:**
* **Using a t-table:** Look up the t-value in a t-table with 3 degrees of freedom. You'll find that 3.635 falls between the values for which you'd find probabilities.
* **Using a calculator or software:** We can use the cumulative distribution function (CDF) of the t-distribution. The P-value is 1 - CDF(t, df).
**Calculation**
Using Python (scipy.stats):
```python
import scipy.stats as stats
t_stat = 3.635
n = 4
degrees_of_freedom = n - 1
p_value = 1 - stats.t.cdf(t_stat, df=degrees_of_freedom)
print(f"The p-value is: {p_value:.4f}")
```
The p-value is approximately 0.0179.
**Answer**
The P-value is approximately 0.0179.
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