Download Hypothesis test for the difference of population means: t test An

Hypothesis test for the difference of population means: t test An industrial plant
wants to determine which of two types of fuel, electric or gas, 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 11 plants
using electricity, which had a mean cost per unit of $37.2 and standard deviation of
$7.87, and 9 plants using gas, which had a mean of $46.5 and standard deviation of
$8.69. 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. Can
we conclude, at the 0.05 level of significance, that the mean cost per unit for plants
using electricity, u1 is less than the mean cost per unit for plants using gas u2?
Perform a one-tailed test. Then fill in the table below. Carry your intermediate
computations to at least three decimal places and round your answers as specified
in the table.
The null hypothesis: H0: µGas= µElectricity
The alternative hypothesis: H1: µGas> µElectricity
The type of test statistic: Independent samples t-test
If t or chi-square test statistic, degrees of freedom: df=n-2=18
If f test statistic, degrees of freedom: dfn__n/a_____ and dfd__n/a_____
The value of the test statistic (Round to at least three decimal places.) 2.484
t= µGas- µElectricity/SEdifference
SEdifference= square root[(sdGas2/nGas) + (sdGas2/nGas)]=3.744
t=9.3/3.744=2.484
The p-value: .0115
Can we conclude that the mean cost per unit for plants using electricity is less than
the mean cost per unit for plants using gas?
Yes, we reject the null hypothesis that the average cost between the two types of
plants are equal and conclude that plants using electricity are more cost efficient
than plants using gas.