Two different formulations of an oxygenated motor fuel are being tested to study their road octane numbers. the variance of road octane number for formulation 1 is
σ1²=1.5
, and for formulation, 2 it is
σ2²=1.2
. two random samples of size
n1=15andn2=20
are tested, and the mean road octane numbers observed are
ẋ1=89.6
and
ẋ2=92.50
assume normality.
a. if formulation 2 produces a higher road octane number than formulation 1, the manufacturer would like to detect it. formulate and test an appropriate hypothesis using α = 0.05. what is the p-value?
b. explain how the question in part (a) could be answered with a 95% confidence interval on the difference in mean road octane number.
c. what sample size would be required in each population if you wanted to be 95% confident that the error in estimating the difference in mean road octane number is less than 1?

answer with step-by-step explanation:

a. ∠j is supplementary to ∠k - true:

(opposite angles of a trapezoid are supplementary which means that they add up to 180 degrees)

b. kl is parallel to jm - true:

(opposite sides are parallel to each other in a trapezoid)

c. jk is perpendicular to kl - false:

(clearly, jk does not make a right angle with kl)

d. jk is parallel to lm - false:

(jk and lm are two lines opposite in direction to each other so they cannot be parallel)

e. ∠j is congruent to ∠m - true:

(the angles on each side of the base are congruent)

f. ∠j is congruent to ∠k - false:

(the angles on the same side but opposite side of the base are not congruent)

ok

step-by-step explanation:

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47