The t-distribution is typically used in the following situations:

1. When the population mean is unknown: This condition is not sufficient by itself for choosing the t-distribution. The t-distribution is often used when the population standard deviation is unknown, not necessarily the population mean.

2. When the population standard deviation is unknown: This is true. If the population standard deviation is unknown and you're estimating the confidence interval based on sample data, the t-distribution is commonly used, especially when the sample size is small.

3. When the sample size is less than 30: This is true. The t-distribution is often used for smaller sample sizes (typically less than 30), as the sample mean follows a t-distribution due to greater variability and less precision compared to larger sample sizes.

4. When the confidence level is less than 90%: This condition is not a reason to use the t-distribution. The choice of the t-distribution or normal distribution is not directly influenced by the confidence level, but by the sample size and whether the population standard deviation is known.

Correct conditions for using the t-distribution:

• When the population standard deviation is unknown.
• When the sample size is less than 30.

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Would you like further clarification on this, or would you like to explore another concept? Here are a few related questions you might find interesting:

1. How does the sample size affect the choice between the t-distribution and the normal distribution?
2. What assumptions do we make when using the t-distribution for confidence intervals?
3. How do you calculate the confidence interval using the t-distribution?
4. How does the t-distribution differ from the normal distribution as the sample size increases?
5. What happens if the population standard deviation is known? Would we still use the t-distribution?

Tip: Remember that the t-distribution is broader and has heavier tails than the normal distribution, which helps account for the increased uncertainty when the sample size is small or the population standard deviation is unknown.