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 7 weights, and the male sample has 16 weights. The t
-statistic for the test is 0.92204. What is the p
-value? (Give your answer to 4 decimal places.)

p
-value:	Answer 1 Question 1


To calculate the p-value for a two-tailed t-test, we need to determine the degrees of freedom and then use the t-statistic provided (0.92204) to find the corresponding p-value.

### Step 1: Determine Degrees of Freedom (df)
Since we are comparing two independent samples (female and male stoach weights), we use the following formula for the degrees of freedom in a two-sample t-test:

\[
df = \frac{ \left( \frac{s_f^2}{n_f} + \frac{s_m^2}{n_m} \right)^2 }{ \frac{ \left( \frac{s_f^2}{n_f} \right)^2 }{n_f - 1} + \frac{ \left( \frac{s_m^2}{n_m} \right)^2 }{n_m - 1} }
\]

Here:
- \(n_f = 7\) (female sample size),
- \(n_m = 16\) (male sample size),
- \(s_f^2\) and \(s_m^2\) are the sample variances for the female and male groups, respectively.

However, if variances are not provided, we can assume equal variances and use the simpler formula for degrees of freedom:

\[
df = n_f + n_m - 2 = 7 + 16 - 2 = 21
\]

### Step 2: Find the p-value using the t-statistic
Given the t-statistic of 0.92204 and 21 degrees of freedom, we can now find the p-value from a t-distribution table or use statistical software.

Since this is a two-tailed test, we calculate the p-value as:

\[
p = 2 \times P(T > |t|)
\]

Now I will calculate the p-value.

The p-value for the given two-tailed t-test is approximately **0.3670** (rounded to 4 decimal places).

Would you like further details or have any questions?

Here are 5 related questions:
1. How do degrees of freedom affect the p-value in a t-test?
2. What are the assumptions of a two-sample t-test?
3. How do you interpret the p-value in hypothesis testing?
4. What is the significance level commonly used in t-tests?
5. How does sample size influence the outcome of a t-test?

**Tip:** In hypothesis testing, a small p-value (typically < 0.05) suggests strong evidence against the null hypothesis, indicating a statistically significant difference.

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 7 weights, and the male sample has 16 weights. The t-statistic for the test is 0.92204. What is the p-value? (Give your answer to 4 decimal places.)

Learn how to calculate the p-value for a two-tailed t-test comparing adult female and male stoach weights with a sample size of 7 and 16, respectively, and a t-statistic of 0.92204. This guide covers key statistical concepts, including degrees of freedom and t-distribution, suitable for undergraduate statistics students.

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