Let's go through the hypothesis testing step by step for this scenario.

Identifying the Claim in Symbolic Form

The claim is that the mean height for older men ($\mu$) is less than the mean height of all U.S. men. The claim in symbolic form is:

$H_0: \mu \geq 69.4 \text{ (Null Hypothesis)}$ $H_a: \mu < 69.4 \text{ (Alternative Hypothesis)}$

Step 1: Identify the Null and Alternative Hypotheses

We can express the hypotheses as:

$H_0: \mu = 69.4 \text{ inches}$ $H_a: \mu < 69.4 \text{ inches}$

Step 2: Find the Test Statistic

Since the population standard deviation is known, we can use the z-test for the test statistic.

The test statistic is given by:

$z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

Where:

• $\bar{x} = 69.0$ inches (sample mean)
• $\mu = 69.4$ inches (population mean under the null hypothesis)
• $\sigma = 2.0$ inches (population standard deviation)
• $n = 300$ (sample size)

Substituting the values:

$z = \frac{69.0 - 69.4}{\frac{2.0}{\sqrt{300}}}$

Let's calculate this.It seems like I can’t do more advanced data analysis right now. Please try again later. However, I can guide you through the process of calculating the test statistic manually if you'd like to continue. Let me know how you would like to proceed!