Let's break down the problem to find the correct answers:

Part 1: Selecting the appropriate calculator for the question

The toy store wants to estimate a proportion (households with kids) based on a sample (301 out of 600). They are also asked to construct a 99% confidence interval for this proportion.

Thus, the correct option is:

• Confidence Interval for a Population Proportion

Part 2: Finding the confidence interval for the proportion

Given:

• Sample size ($n$) = 600
• Number of households with kids = 301
• Sample proportion ($\hat{p}$) = $\frac{301}{600} \approx 0.50167$
• Confidence level = 99%

The formula for the confidence interval for a population proportion is: $\hat{p} \pm Z \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}$

Where:

• $Z$ is the Z-score corresponding to a 99% confidence level.
• For 99%, $Z = 2.576$.

Step-by-step calculation:

1. Calculate the standard error (SE): $SE = \sqrt{\frac{0.50167 \times (1 - 0.50167)}{600}} \approx \sqrt{\frac{0.50167 \times 0.49833}{600}} \approx 0.0204$

2. Calculate the margin of error (ME): $ME = Z \times SE = 2.576 \times 0.0204 \approx 0.0525$

3. Confidence interval: $0.50167 \pm 0.0525$

   So, the confidence interval is: $(0.449, 0.554)$

Part 3: Answers for each section

a. Confidence interval (open-interval format): $(0.449, 0.554)$

b. Tri-linear inequality format: $0.449 < p < 0.554$

c. Point estimate and margin of error: $p = 0.502 \pm 0.053$

Would you like more details or help with another part of this problem?

Here are 5 related questions to deepen your understanding:

1. How does the Z-score affect the width of the confidence interval?
2. What would happen to the confidence interval if the confidence level was changed to 95%?
3. Can we interpret the confidence interval to make a claim about the entire population?
4. Why do we use the standard error to calculate the margin of error?
5. How would the confidence interval change if the sample size were larger?

Tip: Always round the sample proportion and confidence interval to three decimal places for clarity, especially when communicating results.