Question

Two methods were used to measure fluorescent lifetime of a dye. Are the standard deviations significantly different at 95% confidence level? Are the means significantly different at 95% confidence level?

QUANTITY METHOD 1 METHOD 2

Mean lifetime (ns) 1.382 1.346

Standard deviation (ns) 0.025 0.039

# of measurements 4 4   

Answer 1

Ans:

F statistic=(0.039/0.025)^2=2.434

df1=df2=4-1=3

p-value(2 tailed)=2*FDIST(2.434,3,3)=0.4842

As,p-value>0.05,we fail to reject the null hypothesis and we can not conclude that standard deviations are different.

Hypothesis testing for difference in means(pooled variance t test)

pooled standard deviation=sqrt(((4-1)*0.025^2+(4-1)*0.039^2)/(4+4-2))=0.03276

standard error for difference=0.03276*sqrt((1/4)+(1/4))=0.02316

Test statistic:

t=(1.382-1.346)/0.02316

t=1.554

df=4+4-2=6

p-value=tdist(1.554,6,2)=0.1712

As,p-value>0.05,we fail to reject the null hypothesis.there is not sufficient evidence to conclude that the means are significantly different.