Question

two types of flares are tested for their burning times (in minutes) and sample results are given below.

n1 = 35       n2 = 40
x1= 19.4     x2= 15.1
s1 = 1.4       s2= 0.8

assume we have unequal variance

1)Construct a 95% confidence interval for the differences μ_X - μ_Y based on the sample data

2)Interpret the 95% confidence intervall

Answer 1

Answer:

Given,

Sp = sqrt(((n1-1)s1^2 + (n2-1)s2^2)/(n1 + n2 - 2))

substitute values

= sqrt(((35-1)1.4^2 + (40-1)0.8^2)/(35+40-2))

= 1.1202

t(alpha , df) = t(0.05 , 73) = 1.99

95% CI = (x1 - x2) +/- t*Sp*sqrt(1/n1 + 1/n2)

substitute values

= (19.4 - 15.1) +/- 1.99*1.1202*sqrt(1/35 + 1/40)

= 4.3 +/- 0.5160

= (3.784 , 4.816)

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