Which of the following statements is true about prediction intervals and confidence intervals for Y in simple linear regression?

A) A 95% prediction interval for Y given a specific value of the X variable in a regression model is calculated using the formula

y with bar on top plus-or-minus 2 fraction numerator s over denominator square root of n end fraction ,where s is the sample standard deviation, y with bar on top is the sample mean, and n is the sample size. A confidence interval for the mean value of Y replaces the value of "2" with 1.96.

B) If a 95% prediction interval contains 0, we will be able to reject the hypothesis H subscript 0 : beta subscript 1 equals 0 at the 0.05 level of significance.

C) A prediction interval gives a range of "reasonable" values for the actual (new) value of the Y variable, given a specific choice of the X variable. It will, in general, always be narrower than a confidence interval for the mean value of the Y variable because it is easier in general to predict a specific value than to estimate a mean.

D) A prediction interval gives a range of "reasonable" values for an actual (new) value of the Y variable, given a specific choice of the X variable, while a confidence interval gives a range of "reasonable values" for the mean of the Y variable, given a specific choice of the X variable.

E) A prediction interval gives a range of "reasonable" values for the mean value of the Y variable, given a specific choice of the X variable, while a confidence interval gives a range of "reasonable values" for an actual (new) value of the Y variable, given a specific choice of the X variable.