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A group of researchers on Sable Island are wondering whether the grey seals pups on the west side of the island grow at diffeWhat are the degrees of freedom of the test statistic? [1 pt(s)] Submit Answer Tries 0/3 Calculate the standard error of the

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Answer #1

let west side is sample 1

so we have n1=20 sample mean =m1=32.840 sample SD=S1=14.524

let east side is sample 2

so we have n2=22 sample mean =m2=26.009 sample SD=S2=11.306

1.

since we are testing that if there is difference in mean weight or not hence

H_0: \mu_1=\mu_2,H_a: \mu_1 \neq \mu_2

since we do not have knowledge about true standard deviation hence

we will use

t distribution

since it is assumed that both variances are equal hence

DF=n1+n2-2=20+22-2=40

standard error of test statistics is given by

SE=\sqrt{\frac{(n1-1)S1^2+(n2-1)S2^2}{n1+n2-2}*(\frac{1}{n1}+\frac{1}{n2})}

=\sqrt{\frac{(20-1)*14.524^2+(22-1)*11.306^2}{20+22-2}*(\frac{1}{20}+\frac{1}{22})}=2.66

now test statistics is given

t=\frac{m1-m2}{SE}=\frac{32.840-26.009}{2.66}=2.57

P Value =2*P(t>2.57) =2*0.007=0.014

Since P Value is less than level of significance hence

we reject H0

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