Conclusion there is no evi dence that captive

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Conclusion: there is no evi- dence that captive Humboldt penguins have a bill length any different from wild penguins (6.4cm). 5. (16 pts) Consider H : p = 0 . 32 vs the two-sided alternative H A : p 6 = 0 . 32, where p is the gerni- mation rate of oriental bittersweet seeds in tulip poplar stands. The number of seeds that germi- nate, out of 120 seeds, has a binomial B (120 , . 32) distribution if the null hypothesis is true, which is approximated by a normal N (38 . 4 , 5 . 11 2 ) distri- bution ( np = 38 . 4 and nq = 81 . 6 are both > 5). We observe z = (58- 38 . 4) / 5 . 11 = 3 . 835 (or X 2 = 14 . 71 with a chi-square test) so that the p-value is p = 2 * . 00006 = 0 . 0001. There is very strong evidence that the germination rate in tulip poplar stands is greater than 0 . 32. 6.(a) (6 pts) Binomial B (10 , . 72), skewed left. (b) (5 pts) 0 . 180 (c) (5 pts) 0 . 18 + 0 . 18- . 18 * . 18 = 0 . 327 because the two events are not mutually exclusive. We can calculate the probability of finding oriental bittersweet in exactly 6 plots out of 10 in both locations (0 . 18 * . 18) because these events are independent. (d) (10 pts) We may argue for a one-sided test, H A : p r < . 72 because of the scientist’s suspicion. We are not told, but this suspicion could be based upon prior data. H : p r = 0 . 72. The number of plots where oriental bittersweet is present has a binomial distribution X r ∼ B (10 , . . 32) if the null hypothesis is true, with an expected value of 3.2. The values that are as extreme as or more extreme than what was observed are x = 0 and x = 1, so the p-value is P ( X r = 0) + P ( X r = 1). Using the binomial formula, we get . 000003 + . 000076 = 8 . 10- 5 . (we could double this by two for a two- sided test). There is very strong evidence that p r < . 32. Frequency 20 40 60 80 100 10 20 30 40 Summary of grades ● ● ● ● ● 63 75 84 1...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online