(6 points) Twenty (20) rats were paired according to certain salient characteris

Question

(6 points) Twenty (20) rats were paired according to certain salient characteristics so that the 10 pairs have similar conditions. The members of each pair have been randomly assigned to diet 1 or diet 2. The lifetime (days)of the 10 pairs of rats are shown in the table below: 1. Rat Pairs Diet 1 1271 1311 1221 1275 1221 1289 1291 1393 1224 1223 Diet 2 1267 1359 13121247 1279 1388 1296 1343 1402 1365 Is there sufficient evidence that Diet 2 leads to longer lifetime on average than Diet 1? Assume both populations are normally distributed.

Explanation / Answer

Ans:

Test statistic:

t=(53.9-0)/(74.44/sqrt(10))

t=2.290

df=10-1=9

p-value=tdist(2.290,9,1)=0.0239

Assume significance level=0.05

As,p-value<0.05,we reject the null hypothesis.

There is sufficient evidnece to conclude that Diet 2 leads to longer lifetime on avearge than Diet 1.

Diet 1 Diet 2 d 1 1271 1267 -4 2 1311 1359 48 3 1221 1312 91 4 1275 1247 -28 5 1221 1279 58 6 1289 1388 99 7 1291 1296 5 8 1393 1343 -50 9 1224 1402 178 10 1223 1365 142 mean= 53.90 std. dev= 74.44

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