Question

Listed below are body temperatures of four subjects measured at two different times in a day:

Body Temperature (°F) at 8 AM on Day 1	98	97.0	98.6	97.4
Body Temperature (°F) at 12 AM on Day 1	98	97.6	98.8	98.0

Assume that you want to use a 0.05 significance level to test the claim that the paired sample data come from a population for which the mean difference is . Find , , the   test statistic and the critical values.

Answer 1

The necessary calculations done below,

98 98 Before(At 8AM) After (At 12 AM) d=After-Before (d-dbar)^2 0 0.1225 97 97.6 0.6 0.0625 98.6 98.8 0.2 0.0225 97.4 98 0.6 0.0625 sum 1.4 0.27 dbar=sum(dy10 0.35

Here,

before=Body Temperature (0F) at 8 AM on Day 1

After=Body Temperature (0F) at 12 AM on Day 1

we want to test,

Ho: The paired samples data comes from a population for which the mean not differences.

H1: : The paired samples data comes from a population for which the mean difference.

Test Statistic,

here, s^2 = sum((d-dbar)^2)/(n-1)) = 0.27/3 = 0.09

t= dbar/ sqrt(s^2 / n) = 0.35 /sqrt(0.09/4) = 2.3333

Critical value,

t(0.025)=3.182

Decision: t=2.3333< t(0.025)=3.182 , we may fail to reject null hypothesis,

Conclusion, There is insufficient evidence to onclude that the paired samples data comes from a population for which the mean differences.