Stoaches are fictional creatures, sometimes mistaken for mome raths.

Suppose a two-tailed t
-test is conducted to test for a difference between the population means of adult female stoach weights and adult male stoach weights. The female sample has 12 weights, and the male sample has 23 weights. The t
-statistic for the test is -0.38627. What is the p
-value? (Give your answer to 4 decimal places.)

To calculate the p-value for a two-tailed t-test, given the t-statistic, we need the degrees of freedom (df) and the t-statistic itself. In your problem, the t-statistic is \( t = -0.38627 \), and we have two independent samples.

### Step 1: Degrees of Freedom
The degrees of freedom for two independent samples are calculated using the following formula:

\[
df = \frac{ \left( \frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} \right)^2 }{ \frac{ \left( \frac{s_1^2}{n_1} \right)^2 }{n_1 - 1} + \frac{ \left( \frac{s_2^2}{n_2} \right)^2 }{n_2 - 1} }
\]

However, if we do not have the sample variances \( s_1^2 \) and \( s_2^2 \), we can use a simpler approximation, assuming equal variances and combining the sample sizes:

\[
df = n_1 + n_2 - 2
\]

Here, \( n_1 = 12 \) and \( n_2 = 23 \).

\[
df = 12 + 23 - 2 = 33
\]

### Step 2: p-value Calculation
The p-value is obtained from the t-distribution based on the degrees of freedom and the absolute value of the t-statistic. Since this is a two-tailed test, we look at both ends of the distribution.

Now, let’s calculate the p-value using the t-statistic \( t = -0.38627 \) and \( df = 33 \). 

I will compute it.The p-value for the two-tailed t-test with a t-statistic of \(-0.38627\) and 33 degrees of freedom is approximately \(0.7018\).

Would you like further details on this calculation, or do you have any other questions?

Here are 5 related questions to explore:
1. What does a p-value indicate in hypothesis testing?
2. How does sample size affect the t-statistic and p-value?
3. What is the difference between a one-tailed and two-tailed test?
4. How do you calculate the degrees of freedom in more complex t-tests?
5. What assumptions underlie the independent two-sample t-test?

**Tip:** A high p-value suggests that there is weak evidence against the null hypothesis, implying that the difference between means may not be statistically significant.

Suppose a two-tailed t-test is conducted to test for a difference between the population means of adult female stoach weights and adult male stoach weights. The female sample has 12 weights, and the male sample has 23 weights. The t-statistic for the test is -0.38627. What is the p-value? (Give your answer to 4 decimal places.)

Find out how to calculate the p-value for a two-tailed t-test comparing the weights of adult female and male stoaches. This problem involves using the t-statistic, degrees of freedom, and t-distribution concepts. Perfect for undergraduate students studying statistics or hypothesis testing.

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