Question

[5 total pt(s)] Grey seals are capital breeders and stay with their pups until they are weaned. A group of researchers on Sable Island are interested in seeing whether there is a significant difference in the weight of one week old grey seal pups versus two week old pups. They measured the weight of 23 one week old pups, then weighed those same pups again one week later. The researchers found the average weight of adult female grey seals was 238.31 kg, the average weight of one week old pups was 32.01 kg and the average weight of two week old pups was 31.63 kg. The variance of the difference between the one week and two week pup weights was found to be 18.54. Which of the following would be the reasearcher's correct null hypothesis? Ho: Mi = 2 O Ho: Vi <H2 O Ho: Mi = H2 = 30 Ho: Mi # H2 [1 pt(s)] Submit Answer Tries 0/1 Which of the following is the correct alternative hypothesis? O Ha: Vi = P2 O Ha: Pi>H2 Ha: Hi # 2 O Ha: Vi < V2 [1 pt(s)] Submit Answer Tries 0/1

Answer 1

$H_0:\mu_1=\mu_2\\ H_1:\mu_1\neq \mu_2\\ Test~statistic=t=\frac{\sqrt{n}(\bar{x}_1-\bar{x}_2)}{s_d}=0.4232\\\\ where,~n=23,~\bar{x}_1=32.01,~\bar{x}_2=31.63,~s_d^2=18.54\\\\ 95\%~CI~for~difference:~\left( \bar{x}_1-\bar{x}_2-t_{0.025,22}\times \frac{s_d}{\sqrt{n}},~\bar{x}_1-\bar{x}_2+t_{0.025,22}\times \frac{s_d}{\sqrt{n}}\right )\\\\ =(-7.6374,~8.3974);\\\\ ~where,~t_{0.025,22}=2.0739~(R~code:~round(qt(1-0.025,22),4)).\\\\ Since~p-value=2P(t>0.4232|t\sim t_{22})=0.6763>0.05\\\\ (R~code:~round(2*(1-pt(0.4232,22)),4))\\\\ No,~we~fail~to~reject~the~null~hypothesis.$