**Expert Solution:**

In order to calculate the p-value, we will use the standard normal table.
According to the given information, the value of the test statistic is given as:
\[ z = -1.74 \]
Null hypothesis $H_o$ is given as:
\[ p = 0.5 \]
Alternative Hypothesis $H_a$ is given as:
\[ p < 0.5 \]
The formula for p-value is given as:
\[ p = P (Z < z) \]
Where **P**is the probability: \[ p = P (Z < -1.74) \] The p-value can be calculated by determining the probability less than -1.74 using the standard normal table. Therefore, from the table p-value is given as:

**\[ p = 0.0409 \]**

**Alternative Solution:**

For the given problem, the p-value will be determined using the standard probability table. Check against the row starting with -1.74 and column with 0.04. The answer obtained will be:
\[ p = P ( Z< -1.74) \]
**\[ p = 0.0409 \]**

**Therefore, the p-value for $H_a$ < 0.5 is 0.0409.**

**Example:**

For a test of $H_o$: \[ p = 0.5 \], the $z$ test statistic equals 1.74. Find the p-value for
\[ H_a: p>0.5 \].
In this example, the value of test statistic $z$ is 1.74, therefore, it is a right tail test.
For calculating the p-value for a right tail test, the formula is given as:
\[ p = 1 – P ( Z > z) \]
\[ p = 1 – P ( Z > 1.74) \]
Now use the standard probability table to find the value.
The p-value is given as:
\[ p = 1 – 0.9591 \]
\[ p = 0.0409 \]
Therefore, the p-value is**0.0409**.

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