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How do the theoretical results play a role?

Instead of simulating a null distribution (using permutations), the t-distribution can be used to calculate p-values and confidence intervals. The theoretical result provides a t-distribution fit for the sampling distribution of the standardized slope statistic. Why does it matter if the sampling distribution is accurate?

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If the distribution is wrong, the software will not compute a p-value.

If the distribution is wrong, the p-value will not represent the probability of the data given the null hypothesis is true.

If the distribution is wrong, the CI procedure will not capture the true parameter in 95% of samples.

All of the above.

Some of the above.

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