Question

in a random sample of 150 turtles, it is found that 30 have light-coloured shells. let p be the population proportion of turtles that have light-coloured shells.

i) using our observations as a pilot study, estimate the sample size needed to construct confidence interval such that we are 90% confident that the sample proportion will be within 0.01 of the true population proportion p.

ii) if we were to test the hypothesis H0 : p <= 0.15,H1 ; p > 0.15, compute (or bracket) the p-value within the accuracy of the tables

Answer 1

hii... although I am trying to provide the detailed answer but if you have any doubt please ask by comment. please like the answer. thanks...

n=150 X = 30 30 => Â =-*- = 0.2 150 . for go% Confidno deo) 2012 - 20.05 = 1.695 M. E= 0.01 WIT foo b m. E= Zen Tollb) We use estimate of pie, ß instead of b. M. E = 24, TocI-BI =) 1.695 * 10:20)-0 =) 0.2()-0:2) = 0.01 =) n = 4329.64 n 4330 Ho peo15 VIR H,. p>0:15 (ii) to test the test stadisar z = Ê - b 0.2 -OS = 1.71 JOLID 015(1-0'15) 150 P-value = = P(z=1.719): 22000, I) = 0.043264