Question

Managers of an industrial plant want to determine which of two types of fuel, gas or electric, is more cost efficient (measured in cost per unit of energy). Independent random samples were taken of plants using electricity and plants using gas. These samples consisted of 14 plants using electricity, which had a mean cost per unit of $54 and standard deviation of $7.82, and 12 plants using gas, which had a mean of $54.7 and standard deviation of $8.61. Assume that the populations of costs per unit are normally distributed for each type of fuel, and assume that the variances of these populations are equal. Construct a 95% confidence interval for the difference −μ1μ2 between the mean cost per unit for plants using electricity, μ1, and the mean cost per unit for plants using gas, μ2. Then complete the table below.

What is the lower limit of the 95% confidence interval?

What is the upper limit of the 95% confidence interval?

Answer 1

Answer

using Ti-84 calculator

STAT>TESTS>2-SampTInt

enter the data

x1 = 54

s1 = 7.82

n1 = 14

x2 = 54.7

s2 = 8.61

n2 = 12

c-level = 0.95

Pooled: yes

press enter, we get

lower limit = -7.351

upper limit = 5.951