A comparison of the wearing out quality of two types of tyres was obtained by road testing. Samples of 100 tyres were collected. The miles traveled until wear out were recorded and the results given were as follows
Tyres T1 T2
Mean x¯_{1} = 26400 miles x¯_{2} = 25000 miles
Variance S^{2}1= 1440000 miles S^{2}2= 1960000 miles
Determine a confidence interval at the confidence level of 70 percent
Solution
x¯_{1} = 26400
x¯_{2} = 25000
Difference between the two means
(x¯_{1} - x¯_{2}) = (26400 - 25000)
= 1,400
Again we consider the absolute value of the difference among the two means
We calculate the standard error as given below:
S_{(}_{x¯}_{A}_{ - x¯}_{B)} = √{(s^{2}_{1}/n_{1}) + (s^{2}_{2}/n_{2})}
= √{(1,440,000/100) + (1,960,000/100)}
= 184.4
Confidence level at 70 percent is read from the normal tables as 1.04 (Z = 1.04).
Thus the confidence interval is calculated as given below:
= 1400 ± (1.04) (184.4)
= 1400 ± 191.77
or (1400 - 191.77) to (1400 + 191.77)
1,208.23 ≤ X ≤ 1591.77