Computing Confidence Intervals and Conducting Hypothesis Tests in Applied Mathematics

APPLIED MATHEMATICS
STUDENT ID:
[Pick the date]

c) i) The objective is to compute the 95% confidence intervals for both groups. This has been
done below.
Group 1: Control group
Mean = 12.2 days
Standard deviation = 1.9 days
Sample size = 45 mice
Standard error = standard deviation / sqrt (sample size) = 1.9/sqrt(45) = 0.283
Degree of freedom = sample size -1 =45-1= 44
The t value for 95% confidence interval = 2.015
Lower limit = Mean – (t value * standard error) = 12.2 – (2.015* 0.283) = 11.63
Upper limit = Mean + (t value * standard error) = 12.2 + (2.015* 0.283) = 12.77
The 95% confidence interval =[ 11.63 12.77]
Group 2: Treatment Group
Mean = 13.60 days
Standard deviation = 1.78 days
Sample size = 9 mice
Standard error = standard deviation / sqrt (sample size) = 1.78/sqrt(9) = 0.595
Degree of freedom = sample size -1 =9 -1 =8
The t value for 95% confidence interval = 2.306
Lower limit = Mean – (t value * standard error) = 13.6-(2.306*0.595)= 12.23
Upper limit = Mean + (t value * standard error= 13.6+(2.306*0.595)= 14.97
The 95% confidence interval =[ 12.23 14.97]