Sample Quantiles 40 -40 -20 0 20 20 6) Match the q-q plots on the next page with the appropriate letter: (A) skewed left (D) long tailed but symmetrical (B) skewed right (E) short tailed (C) approximately normal Sample Quantiles 1- 0 1 2 2- -2 -1 PLOT 1 -2 -1 0 1 2 Theoretical Quantiles 0 PLOT 3 Theoretical Quantiles 1 2 0.2 0.4 0.6 0.8 1.0 Sample Quantiles 00 0.0 2 Sample Quantiles L 0 3 4 5 -2 -1 PLOT 2 Theoretical Quantiles PLOT 4 -1 0 1 2 Theoretical Quantiles 1 2 7) Let's use the the data above for male kestrel length. Here are the data again, but sorted to help you. Most of the normal scores are also given: Length(cm): 19.1 19.9 20.3 21.2 21.7 22.4 23.2 23.2 24.1 Z-scores: -0.748 -0.473 -0.230 0.000 0.230 0.473 0.748 (a) Calculate the missing normal scores (the first two and the last two). (b) Now construct a q-q plot (normal probability plot). Do this by hand. 24.2 24.6 For all these problems you need to clearly state Ho, H, give a (if not given), and clearly state your conclusion (in words!). 1) Use R for all parts of this problem. Use the data on heights you collected a few weeks ago. (a) Do a t-test and test the following: Ho: =y for your recitation section vs. H: y Use a = .01 (if, for example, your y = 64.72, then you would do Ho: = 64.72) (c) now repeat but add 4.75 to your (so you'd do Ho: =69.47 (= 64.72 +4.75)) (d) repeat (c) but use a = .00000000001 (but see part (e) before you do this). (e) Why do you not need to tell R about a? Make sure you understand this!! (f) what kind of error did you probably make in part (d)? (Just write out the answer for this question). R instructions: To test, for example, that = 64.72, you need to give R the value of : t.test(height,mu = 64.72) (assuming you named your variable "height"; of course, you may have to do data$height or something similar depending on how you have your data in R). Since R gives you p-values (= probabilities) you don't need to calculate or use r* (although R automatically prints this if you want to use it). Do not use R for the rest of the problems: 2) You want to figure out if there is a difference in lengths between male and female kestrels (kestrels are small falcons found all over Northern Virginia). You catch 12 females and 11 males with the following results (in cm): Females: Males: 27.7 25.4 26.4 28.5 27.4 28.0 28.7 26.7 25.6 25.3 27.5 27.8 20.3 24.1 24.6 23.2 22.4 23.2 21.2 24.2 19.1 19.9 21.7 (a) Is there a difference in lengths? Use a = .01. Note that you have to calculate everything yourself. Make sure you give Ho and H (symbols are okay), and clearly write out your conclusion. height handed 68 left 68 right 70 right 63 right 60 right 63 right 63 left 64 right 66 right 71 right 68 left 61 right