Hint Sheet for 4/12/2004 HW

AP Statistics / Mr. Hansen
4/9/2004

Name: _________________________

#14.2(a)	This is review of LSRL techniques from earlier in the year. I assume you still remember how to do this, and if not, then this is your chance to re-teach yourself.

(b)	More LSRL review. Show your work so that I can see that you actually added the residuals.
(c)	Remember that we use Greek letters for parameters, Roman letters for their “statistical” counterparts. For example: s = true s.d., whereas s = sample s.d. computed from data m = true mean, whereas xbar = sample mean computed from data r = idealized (parameter) regression coefficient, whereas r = computed regression coefficient In the same fashion, our LSRL expression, yhat = a + bx, becomes a + bx when we use the idealized (parameter) versions of a and b. Remember, a = LRSL intercept and b = LSRL slope when you use STAT CALC 8. The AP formula sheet muddies the water somewhat by using b₀ for intercept and b₁ for slope. Can you make the equivalence to a and b in your mind? Good. Unfortunately, every rule seems to have an exception. The exception to this “Greek/Roman” rule appears when we discuss proportions: p = true population proportion (i.e., probability), but phat = sample proportion Getting back to the problem, the question is asking you to estimate the “true” intercept (a), the “true” slope (b), and the “true” s.d. of y (s) based on the corresponding Roman-letter versions that your calculator spits out when you use STAT TESTS E. Surely you can do this. What your calculator calls s is the same as what your book calls s. Thank goodness for that. Warning: There is another quantity that is of interest in the later questions, namely the standard error of the slope. Your book calls this SE_b, but the AP formula sheet uses the symbol s_b₁. (Actually, AP says “s subscript b subscript 1,” but I don’t have the ability to show a subscript of a subscript here!) You might ask, “Mr. Hansen, what symbol does my calculator use for s_b₁? The answer is that you have to compute it yourself. However, do not be tempted to use the formula on the AP formula sheet. Instead, compute s_b₁ by using the much simpler formula s_b₁ = b₁/t. In other words, divide the computed LSRL slope by the LSRL t-value to get s_b₁. Whew! That’s a lot easier, isn’t it? In computer printouts, s_b₁ is usually shown, though of course it is never labeled with total clarity. (That would be too logical.) In #14.6, s_b₁ = 0.0751, and in Example 14.7, s_b₁ = 0.2300. You can verify that the formula works in Example 14.7, since b₁/t = 0.687747/2.99 does indeed give 0.2300. We will discuss in class exactly why this works. For now, just put the formula s_b₁ = b₁/t into your bag of tricks.

#14.8(a)	More LSRL review. Don’t try claiming you need to be an expert on §14.1 to do this problem. If you can’t do part (a) by now, you are in deep trouble.

(b)	The first half of this question is LSRL review. The second half is a bit tricky and requires a hint. Here is your hint: Use our universal formula for C.I. (no, I’m not going to tell you what it is) and plug in s_b₁ as shown in the printout, along with t* from Table C at the end of your book. Your calculator does not have a built-in feature to do this for you.

#14.9(a)	LSRL review.

(b)	You might be tempted to say b, but remember that the question asks for a parameter.

(c)	Similar to #14.8(b). In fact, if you couldn’t do #14.8(b), you might consider using the answer key for #14.9(c) as a guide to reverse-engineer a solution for #14.8(b).