Question

Two types of flares are tested and their burning times are recorded. The summary statistics are given below: n = 35 n = 40 = 19.4 min = 15.1 min s = 1.4 min s = 0.8 min Construct a 95% confidence interval for the differences between the mean burning time of the brand X flare and the mean burning time of the brand Y flare.
a. 3.2 min < ?X - ?Y < 5.4 min
b. 3.6 min < ?X - ?Y < 5.0 min
c. 3.8 min < ?X - ?Y < 4.8 min
d. 3.5 min < ?X - ?Y < 5.1 min

Answer 1

Answer:

C. 3.8 min < ?X - ?Y < 4.8 min

Step-by-step explanation:

Let both flares be X and Y

For X

n1 = 35

Bar x1 =19.4

D1 = 1.4

For Y

n2 = 40

Bar X2= 15.1

S2 = 0.8

√(x1²/n1) + (x2²/n2)

=√ (1.4²/35)+(0.8²+40)

= 0.2683

Critical value, t = 2.032

We now have to calculate margin of error

0.2683x2.032

= 0.545 this is approximately equal to 0.5

Bar x1 - bar X2

= 19.4 - 15.1

= 4.3

At 95% confidence level

4.3+-0.5

4.3+0.5= 4.8

4.3-0.5 = 3.8

Therefore the answer is 3.8min<X-Y<4.8min