Toby wants to know the average price of new cars at a particular dealearship. He randomly selects a sample of 33 cars and finds that the average price to be 
 with a standard deviation of 
. What is the 95% confidence interval for the mean price of cars at this particular dealership?

a.) Which distribution table will be used to find the critical value and why?

t-table because the population standard deviation is unknown
Z-table because the population standard deviation is known
t-table because the population standard deviation is known
Z-table because the population standard deviation is unknown



To determine which distribution table to use for finding the critical value, consider the following:

- If the population standard deviation is **known**, we use the **Z-table**.
- If the population standard deviation is **unknown** and the sample size is **small (typically n < 30)**, we use the **t-table**.
- If the population standard deviation is **unknown** but the sample size is **large (typically n ≥ 30)**, we also use the **t-table**.

Given the information:
- The population standard deviation is unknown.
- The sample size is 33, which is larger than 30.

Therefore, the appropriate table to use is:

**t-table because the population standard deviation is unknown.**

Would you like more details or have any questions?

Here are 5 numbered questions for you to ask:

1. How do you calculate a 95% confidence interval for the mean?
2. What is the critical value for a 95% confidence interval from the t-table?
3. How does sample size affect the choice of distribution table?
4. Can you explain the difference between the t-distribution and the normal distribution?
5. What is the formula for the margin of error in a confidence interval?

**Tip:** When dealing with sample statistics and unknown population parameters, the t-distribution is generally preferred, especially for smaller sample sizes or when the sample size is just slightly above 30.

Learn how to calculate a 95% confidence interval for the mean price of cars using statistics. This problem involves understanding confidence intervals, sampling, and the Central Limit Theorem. Suitable for advanced high school students or college-level learners.

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