Answer:
The 90 % confidence limits are (-2.09, 8.09).
Since the calculated values do not lie in the critical region we accept our null hypothesis.
Step-by-step explanation:
The null and alternative hypothesis are given by
H0: σ₁²= σ₂² against Ha: σ₁² ≠ σ₂²
Confidence interval for the population mean difference is given by
(x`1- x`2) ± t √S²(1/n1 + 1/n2)
Where S ²= (n1-1)S₁² + S²₂(n2-1)/n1+n2-2
Critical value of t with n1+n2-2= 50+ 35-2= 83 will be -1.633
Now calculating
S ²=34* (12.8)²+ (14.6)²*49/83= 192.96
Now putting the values in the t- test
(75.1 -72.1) ± 1.633 √ 192.96(1/35 +1/50)
=3 ± 5.09
=-2.09, 8.09 is the 90 % confidence interval for the difference
The 90 % confidence limits are (-2.09, 8.09).
Since the calculated values do not lie in the critical region we accept our null hypothesis.
