Question

Determine whether the following statements are true or false. No explanations are needed:

1. The least squares regression line always passes through the point (x̄, y̅), i.e., y̅ = b₀ + b_{1 *} x̅

2. The p-value is the probability of how true the null hypothesis is, given the data. Thus small p-value tends to reject the null hypothesis

3. Instead of a normal distribution, a family of t-distributions is needed for a small sample size with unknown population standard deviation because so to incorporate extra variability involved in such situation.

4. The interpretation of the confidence of a CI is always about the probability of capturing the true unknown population parameter of interest if the random sampling could be done repeatedly under similar situation, although in real application, we just have one random sample only.

5. The p-value is the probability of either making a type I error or a type II error, depending on the decision of the hypothesis test procedure.

Answer 1

The least squares regression line always passes through the point (x̄, y̅), i.e., y̅ = b0 + b1 * x̅

TRUE

The p-value is the probability of how true the null hypothesis is, given the data. Thus small p-value tends to reject the null hypothesis

TRUE

Instead of a normal distribution, a family of t-distributions is needed for a small sample size with unknown population standard deviation because so to incorporate extra variability involved in such situation.

TRUE

The interpretation of the confidence of a CI is always about the probability of capturing the true unknown population parameter of interest if the random sampling could be done repeatedly under similar situation, although in real application, we just have one random sample only.

FALSE

The p-value is the probability of either making a type I error or a type II error, depending on the decision of the hypothesis test procedure

FALSE

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