Course Notes - Department of Mathematics and Statistics

SOLUTION - Calculating the confidence intervalThe confidence interval is:1(x 1 − x 2 ) ± t (α p√ ,ν)s + 12 n 1 n√ 21(10.298 − 8.066) ± 2.086 × 1.303 ×13 + 1 92.232 ± 1.180That is, 1.05 < µ obese− µ lean < 3.41 MJ/daySOLUTION - Interpreting the confidence intervalThe confidence interval for the difference in energy expenditurebetween the two groups is: 1.05 < µ obese − µ lean < 3.41 MJ/dayThis confidence interval tells us that we can be 95% sure that theTRUE difference in the energy expenditure of obese and lean patientsis between 1.05 and 3.41 MJ/day.We test whether the two means are the same i.e. µ 1 = µ 2 (orµ 1 − µ 2 = 0), by looking for zero in the confidence interval.The confidence interval is entirely positive (does not include zero)hence there is a significant difference in energy expenditure betweenthe two groups. The obese patients consume more energy than thelean patients.We can say that the p-value is less than 0.05, i.e. p < 0.05.NOTES• Both populations should have values which are normally distributedif the samples are small.• The variances should be approximately equal.• The samples from the two populations should be random andindependent of each other.• This procedure is sometimes called the unpaired t-test.105