Answer must be typed for 4 decimal Consider the following da

Answer must be typed for 4 decimal

Consider the following data for two independent random samples taken from two normal populations with equal variances. Find the 99% confidence interval for mu1-mu2. (See exercise lion page 449 of your textbook for a similar problem.)

Solution

X (Mean)=8.5; Standard Deviation (s.d1)=2.739
Number(n1)=6
Y(Mean)=12; Standard Deviation(s.d2)=2.3664
Number(n2)=6
Value Pooled variance S^2= (n1-1*s1^2 + n2-1*s2^2 )/(n1+n2-2)
S^2 = (5*7.5021 + 5*5.5998) / (12- 2 )
S^2 = 6.551,
S = sqrt(6.55095) = 2.5594
CI = x1 - x2 ± t a/2 * Sp^2 ( 1 / n1 + 1 /n2 )
Where,
x1 = Mean of Sample 1, x2 = Mean of sample2
sd1 = SD of Sample 1, sd2 = SD of sample2
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x1)=39
Standard deviation( sd1 )=8
Sample Size(n1)=18
Mean(x2)=49
Standard deviation( sd2 )=4
Sample Size(n1)=13
CI = [ ( 8.5-12) ±t a/2 * 2.5594* Sqrt( 1/6 + 1/6 )]
= [ (-3.5) ± t a/2 * 1.477 ]
= [ (-3.5) ± 5.955264 ]
= [-9.4553 , 2.4553]