INVESTIGATING STATISTICAL CONCEPTS, APPLICATIONS, AND METHODS
BRIEF SOLUTIONS
TO INVESTIGATIONS 1.6
(a) answers will vary
(b) probably not
(c) example results
(d) Most likely: 0 or 1,
least likely: 4
(e) should be close to 1
(f) Graph bounces around when the number of trials is small but then begins to converge to .375.
(g) results will vary, should be around .04.
(h) impossible since if 3 mom’s match, the fourth must as well.
(i) should eventually converge to 1.
(j)
1234 1243 1324 1342 1423 1432
2134 2143 2314 2341 2413 2431
3124 3142 3214 3241 3412 3421
4123 4132 4213 4231 4312 4321
(k) 1/24
(l) 2143, 2341, 2413, 3142, 3412, 3421, 4123, 4312, 4321
(m)
4 2 2 1 1 2
2 0 1 0 0 1
1 0 2 1 0 0
0 1 1 2 0 0
(n) There are 9 zero’s so the probability is 9/24.
(o) P(X=1) = 8/24
P(X=2) = 6/24
P(X=3) = 0/24
P(X=4) = 1/24
(p) Answers will vary
(q) should be similar
(r) 15/24
(s) 15/24 = 1-(9/24)
(t) 0(9/24) + 1(8/24) + 2(6/24) + 3(0/24) + 4(1/24) = 24/24 = 1.
(u) should be similar
(v) no, no
Investigation 1.6.2:
Animal Models for Stroke Treatment
(a) X can range from 3 to 7 (since are at most 7 rats in either group)
(b)-(c) results will vary
Example results
(d) It is very surprising to find all 7 in one group (happens about 3% of the time by chance alone)
(e) C(14,7) = 3432
(f) C(10,7) = 120
(g) P(X=7) = 120/3432 = .035, close to the above simulation results
(h) We would be willing to draw a cause and effect conclusion since we have evidence this result didn’t happen just by chance and since it was a randomized comparative experiment, there shouldn’t be any confounding variables.