Question

Problem 10: Bird songs have been hypothesized to be a secondary sexual character signaling an individual's health status. Researchers designed an experiment in which they randomly assigned male collared flycatchers (Ficedula albicollis) to two groups: One group received an immune challenge in the form of an injection of sheep red blood cells and the other group had a placebo injection. Here are the changes in song rate (in strophes per minute) after the injection for 15 male collared flycatchers in the immune- challenge group (ICG) and 12 males in the placebo group (PG). ICG: -1.6,-3.1, -2.7, -3.7-3.1, -3.6,-1.9, -1.5, -0.1, 0.8,-0.1, -0.2, -1.2,-1.9, 0.2 PG: -1.5, 1.7, 0.4,-1.8, 0.0, 0.4, 0.8, 2.0, 0.0,-2.4, -1.5, -0.1 The normal quantile plots of the ICG and PG data suggest that the data approximately follow normal distributions, respectively. The sample mean and sample standard deviation for ICG are - 1.58 and 1.462 and the sample mean and sample standard deviation for PG are -0.1667 and 1.3826 (Brigitte Baldi and David S. Moore, 2018, The Practice of Statistics in the Life Sciences, p. 467). Q1. Construct a 95% confidence interval for the population mean difference (ICG - PG) of song-rate change and write a brief interpretation of your confidence interval in terms of the context. Q2. Do the data support the claim that, on average, an immune-challenge injection reduces more male-song-rate than a placebo injection does at a significance level of 0.05? Answer the question by a) formulating null and alternative hypotheses in terms of the population parameter as well as the context of this application. b) finding the P-value of the test, interpreting your P-value in the context of the application, and making your conclusion

Answer 1

goy confidence interval is given by (e-y I ta, nitn2-2 Sith S= nisu nasz nitz -D S=. I 15x(1.462)² + 12% (1.382672 St12 - 2 1.4832

IS8 1. = -1058 J = -0.1667 - O.1667 ti 12 (-1.58 +0.166 7) = 2:06 X1.4832 Jis - 1.4133. – 1. 1833 (-2.5966 - 0.23). 2la Ho ICG G has has same some 4.=l2 meam meam as PG a le ICG injec - 1 injection reduces more male song rate than PG injection in M, C lz. b) Test Test t= statistic x - - I 4 ~tnith 11thz-2. sti In na +1 2 - 1.58 +0.1667 1.4832 is 12 t - 2.46 . e value = o.olos. 0.010s co.05 Ho is rejected conclude that ICG reduces more song rate than PG injection. and we male