Which of the following statements is true about distributions of slope and its a

Question

Which of the following statements is true about distributions of slope and its associated test statistic for testing Ho: beta_1 = 0?

1) The CLT implies that the sample slope has a normal distribution as long as the sample size is large enough.

2) The CLT implies the sample slope has a t-distribution as long as the sample size is large enough.

3) We only need the CLT to say the test statistic (sample slope) / (std. error of slope) has a normal distribution as long as the sample size is large enough.

4) If the true standard deviation of the sample slope were known, the statistic (sample slope) / (true std.dev. of slope) would have a t-distribution.

Would you agree it is (2) ?

Explanation / Answer

2) The CLT implies the sample slope has a t-distribution as long as the sample size is large enough.

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