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Unformatted text preview: Practice Test 11A Solutions 1) C . t procedures are ALWAYS used for inferences on MEAN(s), and we know that mean is NOT robust (ie., not resistant to outliers), so rule out choice E. The size of the standard deviation has NEVER been one of our conditions to check (the bigger it is, though, the less power and precision we have), so rule out D. The stemplot of our sample data does NOT need to provide evidence that the population is normal. By the C.L.T., as long as our sample size is large enough, the sampling distribution of means will be roughly normal, so rule out A. Same goes for B. Rule it out, since the sampling distribution of means will be roughly normal, if n is sufficiently large, EVEN IF the data gives us evidence that the population is moderately skewed. Therefore, the correct answer is C. t-procedures are not resistant to outliers. 2) C. S.E.M. (standard error of the mean) = n s , so . 5 9 15 = 3) A . right from the table of t values. ALSO, even if it had said with probability .10 to the left of t*, the table would still provide the t critical value, youd just make it - 1.397. 4) A , obviously. The Matched Pairs t-procedures for a single MEAN are used when the two sets of values are DEPENDENT.. this is when we match them. For example, a groups pretest scores and their post-test scores. 5) E. Interesting problem. FOCUS IN, right away, on the length of the confidence interval, 4 cm. What must the margin of error be? A confidence interval for an unknown mean is equal to the estimate (ie, sample mean) plus/minus the margin of error. So if the length of the confidence interval (the distance from the leftbound to the rightbound) is 4, the margin of error must have been TWO. Therefore, we can set up the following equation and solve: n s t * 2 = , .., 25 064 . 2 2 s = . If you are unsure where the 2.064 came from, it is the critical t-value, found in the table of critical t-values, for 95% confidence, and with 24 degrees of freedom. Solving, you might first divide both sides by 2.064, then mutiply both sides by the square root of 25, which is 5, and that yields s=4.84. HOWEVER be careful, the problem asks for variance, which is 2 s , so square your answer and you get 23.47. Theres one other potential pitfall, here, one which is really challenging your reading comprehension skills. What is the difference between (d) and (e)? Well. its the difference between P.P. and S.S., which I hope you know well by now. We have just identified the sample variance, s-squared, not the population variance, sigma-squared. 6) D: This is the tortilla problem. Lets use our TI-83 for this one. This test is a t-test for MEAN, or choice #2 in our calculators menu. The calculator quickly gives us a p-value of ....
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This note was uploaded on 11/03/2011 for the course STATS 101 taught by Professor Smith during the Spring '11 term at University of Colorado Denver.
- Spring '11