Prothrombin time is a measure of clotting ability of blood. For rats treated wit

Question

Prothrombin time is a measure of clotting ability of blood. For rats treated with an antibiotic and 10 control rats, the prothrombin times (in seconds) were reported as follows.

Antibiotic Control

N 10 10

Y 25 23

S 10 8

a. Construct a 90% confidence interval for the difference in population means (issue that the two populations from which the data came are normally distributed) (note: formula (6.7.1) yields 17.2 degrees of freedom for these data

b. why is it important that we assume that the two populations are normally distributed in part a?

B. Interpret the confidence interval from part a in the context of this setting

Explanation / Answer

Calculation

Pooled Variance
s2p = (SS1 + SS2) / (df1 + df2) = 164 / 18 = 9.11

Standard Error
s(M1 - M2) = ((s2p/n1) + (s2p/n2)) = ((9.11/10) + (9.11/10)) = 1.35

Confidence Interval
1 - 2 = (M1 - M2) ± ts(M1 - M2) = 2 ± (1.73 * 1.35) = 2 ± 2.34

Result

1 - 2 = (M1 - M2) = 2, 90% CI [-0.34, 4.34].

You can be 90% confident that the difference between your two population means (1 - 2) lies between -0.34 and 4.34.

b).

In order to construct a confidence interval, we make three assumptions:

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