In this context:

Since the sample size is 7, we need to use the t-distribution, which is appropriate for small sample sizes (generally $n < 30$) when the population standard deviation is unknown.

• The degrees of freedom (df) for the t-distribution are calculated as $n - 1$. So, with a sample size of 7, the degrees of freedom are $7 - 1 = 6$.

Let's correct the statements based on this information:

1. The sample size must be increased. (This is not necessary but may help reduce the margin of error for the estimate.)
2. The t distribution with 7 degrees of freedom must be used. (This is incorrect; it should be 6 degrees of freedom.)
3. The normal distribution can be used. (This is incorrect for a small sample size from a population that is not normally distributed. We should use the t-distribution.)
4. The t distribution with 6 degrees of freedom must be used. (This is correct.)

Corrected Statements:

• The t distribution with 6 degrees of freedom must be used.

Let me know if you want further details or have any questions!

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Here are some additional questions based on this information:

1. Why is the t-distribution used instead of the normal distribution for small samples?
2. How does increasing the sample size affect the interval estimate?
3. What are the properties of the t-distribution as degrees of freedom increase?
4. How would the approach change if the population standard deviation were known?
5. What impact does a non-normally distributed population have on interval estimation?

Tip: When sample sizes are small, using the t-distribution is more reliable than the normal distribution for confidence intervals due to its wider tails, which account for the added uncertainty.