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Let's go through each part of the problem step-by-step.

### Problem Summary
You are given:
- A sample of 28 white-collar employees who work on average \( \bar{x} = 43.73 \) hours per week.
- The population standard deviation \( \sigma = 3.2 \) hours.
- The hypothesis is about whether the mean hours worked per week by white-collar employees is greater than 42 hours.
- The test is to be conducted at a 1% significance level.

### Part (a): Required Assumptions
The assumptions for performing a hypothesis test and constructing a confidence interval on the mean include:
1. Each observation is sampled randomly and independently from the same distribution.
2. The data should be sampled from a distribution that doesn’t deviate far from normality, especially given the population standard deviation is known and the sample size is less than 30.
3. The population mean is unknown.
   
Therefore, **all of the above assumptions are required** for a valid z-test under these conditions. 

### Part (b): Choosing Between z- and t-distribution
Since the population standard deviation (\( \sigma = 3.2 \)) is known, we should use the **z-distribution**. If we did not know \( \sigma \) and only had the sample standard deviation, then we would use a t-distribution.

### Part (c): Hypothesis Test
#### Step i: Parameter of Interest
The parameter of interest here is the **true mean number of hours worked per week by all U.S. white-collar workers**. This is because we are trying to determine if the average working hours of this group exceed 42 hours.

#### Step ii: Hypothesis Statement
Since the question is whether the mean hours worked per week is greater than 42, we have:
- Null Hypothesis \( H_0: \mu \leq 42 \)
- Alternative Hypothesis \( H_a: \mu > 42 \)

Thus, the correct hypothesis statement is:
- **\( H_0: \mu \leq 42, \, H_a: \mu > 42 \)**.

#### Step iii: Test Statistic Calculation
Since we are using a z-test, the test statistic \( Z \) is calculated using:

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

Where:
- \( \bar{x} = 43.73 \) (sample mean),
- \( \mu_0 = 42 \) (hypothesized mean),
- \( \sigma = 3.2 \) (population standard deviation),
- \( n = 28 \) (sample size).

Substitute the values:

\[
Z = \frac{43.73 - 42}{3.2 / \sqrt{28}} = \frac{1.73}{3.2 / 5.2915} = \frac{1.73}{0.6048} \approx 2.86
\]

#### Step iv: Finding the p-value
Using the z-distribution table, we can find the p-value corresponding to \( Z = 2.86 \). For a one-tailed test, the p-value is approximately **0.0021**.

Since the p-value (0.0021) is less than the significance level (0.01), we **reject the null hypothesis**. This suggests there is evidence to support that the mean hours worked per week by white-collar workers is greater than 42.

### Summary of Answers:
1. **(a)** All of the assumptions are required.
2. **(b)** Use a z-distribution.
3. **(c)** 
   - i. True mean number of hours worked per week by U.S. white-collar workers.
   - ii. Hypotheses: \( H_0: \mu \leq 42 \), \( H_a: \mu > 42 \).
   - iii. Test statistic \( Z \approx 2.86 \), p-value \( \approx 0.0021 \).

Would you like additional clarification or further details on any step?

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Here are 5 related questions to deepen your understanding:
1. What would change in the test if the population standard deviation were unknown?
2. How would the sample size affect the test outcome if it were smaller or larger?
3. What is the importance of the significance level in hypothesis testing?
4. How would the hypothesis change if we were testing for the mean being exactly 42 hours?
5. What are Type I and Type II errors in the context of this hypothesis test?

**Tip:** Always check if the population standard deviation is known or unknown before deciding between a z- and t-distribution for your test.

The 40-hour work week did not become a U.S. standard until 1940. Today, many white-collar employees work more than 40 hours per week because management demands longer hours or offers large monetary incentives. A random sample of 28 white-collar employees worked on average 43.73 hours per week. Is there any evidence that the true mean number of hours worked per week by white-collar employees is greater than 42? Assume that the population standard deviation is 3.2 hours. Perform the hypothesis test at a 1% significance level.

Conduct a hypothesis test to determine if the true mean weekly hours worked by white-collar employees is greater than 42. This example uses a z-test with a population standard deviation of 3.2 hours and a sample mean of 43.73 hours for 28 employees, tested at a 1% significance level.

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