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The problem is testing if the mean age at which men first marry has increased since 1960, where the historical mean \(\mu_0\) is 24.3 years. Here’s the breakdown:

1. **Determine \(\mu_0\):**
   Since we are comparing to the 1960 mean age, \(\mu_0 = 24.3\).

2. **Test Statistic Form:**
   For a test comparing a sample mean to a known population mean, we often use a **t-statistic**:
   \[
   t = \frac{\bar{y} - \mu_0}{\text{SE}(\bar{y})}
   \]
   where \(\bar{y}\) is the sample mean, and \(\text{SE}(\bar{y})\) is the standard error of the mean.

3. **Calculate SE:**
   The standard error, \(\text{SE}(\bar{y})\), is estimated as:
   \[
   \text{SE}(\bar{y}) = \frac{s}{\sqrt{n}}
   \]
   where \(s\) is the sample standard deviation, and \(n\) is the sample size.

4. **Degrees of Freedom:**
   For a t-distribution, the degrees of freedom is \(n - 1\), assuming we don’t know the population standard deviation.

**Answer Choice Analysis:**

- **Choice A** is the correct form because it follows a **t-distribution** with degrees of freedom \(n - 1\).
- \(\mu_0 = 24.3\)
- \(\text{SE}(\bar{y}) = \frac{s}{\sqrt{n}}\)

Thus, the correct answer is:
- **Choice A**

In 1960, census results indicated that the age at which men in a certain region first married had a mean of 24.3 years. It is suspected that young people today are waiting longer to get married. We want to find out if the mean age of first marriage has increased since then.

Analyze if the mean age of first marriage has increased since 1960, where the historical mean age was 24.3 years. This problem involves calculating the test statistic using the t-distribution and standard error formulas for hypothesis testing. Ideal for college-level statistics students.

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