There are researchers who want to know if M poisoning in mice is less extreme in...

There are researchers who want to know if M poisoning in mice is less extreme in males. An SRS of one hundred male mice and an independent SRS of one hundred female mice are obtained. The male mice had a sample mean of thirty-nine and a sample standard deviation of eight. The female mice had a sample mean and standard deviation of 40 and 10, respectively. Let u₁ represent the true mean response for the males and u₂ represent the true mean response of the females.

a) You must find a point estimate for the difference that there is between the two population means.

b) Find a ninety-nine percent confidence interval for u1-u2 and explain your results.

Expert Solution

a)

Point estimate of difference = 39 - 40 = -1

b)

SE = sqrt[ (s12/n1) + (s22/n2) ]
(s12/n1)   0.6400
(s22/n2)    1.0000
SE   1.2806

DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] }
[ (s12 / n1)2 / (n1 - 1) ]            0.004
[ (s22 / n2)2 / (n2 - 1) ]           0.01
(s12/n1 + s22/n2)2           2.69
DF =    189

t value at 99% = 2.602

CI = (x1- x2) +/- t *sqrt(s1^2/n1+s2^2/n2)
= ( 39 -40) +/ 2.602 *sqrt(8^2/100 + 10^2/100)
= (-4.3325 , 2.3325 )

The 99% CI is (-4.3325 , 2.3325 )

orchestra answered 1 year ago

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