Stoaches are fictional creatures that feed on funistrada.

According to Wikipedia, adult stoach weights are normally distributed, with a mean of 432 g and a standard deviation of 43 g.

You weigh a random sample of 73 stoaches, and find a sample mean weight of 433.2 g.

Assume Wikipedia is correct about the standard deviation. What is the 𝑝𝑝-value for a two-sided hypothesis test that Wikipedia is also right about the mean weight? (Give your answer to 4 decimal places.)

To calculate the \( p \)-value for the two-sided hypothesis test, we'll proceed with similar steps as before.

### Step 1: State the hypotheses
- **Null hypothesis (\( H_0 \))**: The population mean weight of stoaches is 432 g.
- **Alternative hypothesis (\( H_1 \))**: The population mean weight of stoaches is not 432 g.

### Step 2: Calculate the test statistic
The test statistic for the sample mean is calculated using the \( z \)-score formula:

\[
z = \frac{\bar{x} - \mu_0}{\frac{\sigma}{\sqrt{n}}}
\]

where:
- \( \bar{x} \) is the sample mean (433.2 g),
- \( \mu_0 \) is the hypothesized population mean (432 g),
- \( \sigma \) is the population standard deviation (43 g),
- \( n \) is the sample size (73).

Let's plug in the values:

\[
z = \frac{433.2 - 432}{\frac{43}{\sqrt{73}}}
\]

### Step 3: Calculate the \( z \)-value
We'll now calculate this \( z \)-value.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you need help with anything else or have questions, feel free to ask!

Learn how to calculate the p-value for a two-sided hypothesis test on stoach weight, using sample mean, population mean, and standard deviation. Understand the application of normal distribution in hypothesis testing. Ideal for advanced high school or college students studying statistics.

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