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.

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

step-by-step explanation:

how many centimeters did the level of the salsa go down by?

idk idk idk idk idk

step-by-step explanation: