In an experiment reported in the Lancet on the effectiveness of isoniazid as a treatment for leprosy in rats, the log survival times (weeks) were evaluated. For untreated rats, the log times were...

In an experiment reported in the Lancet on the effectiveness of isoniazid as a treatment for leprosy in rats, the log survival times (weeks) were evaluated. For untreated rats, the log times were 1.40, 1.46, 1.48, 1.52, 1.53, 1.53, 1.56, 1.58, 1.62, and 1.65. For treated rats, they were 1.71, 1.72, 1.83, 1.85, 1.85, 1.86, 1.86, 1.90, 1.92, and 1.95. The rats were randomly assigned to the two groups, so the groups are independent. If log times in the untreated group are called X₁
and in the treated group are called X₂, the sample means and sums of squares of deviations are X₁
= 1.533, X₂
= 1.845,
(X_I
-X₁)²
= .050, and ∑(X₂
- x₂)²
=,054. Calculate (a) sp; (b) the degrees of freedom; and (c) a 99% confidence interval for the true mean difference in log units: (d) On the basis of the interval obtained in (c), do you feel reasonably sure that the treatment was effective? Why?