Correct | 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 8 plants using electricity, which had a mean cost per unit of $69.40 and standard deviation of $8.44, and 7 plants using gas, which had a mean of $57.30 and standard deviation of $8.56. 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 0.01 level of significance, that Wy the mean cost per unit for plants using electricity, differs from My, the mean cost per unit for plants using gas? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) (a) State the null hypothesis /|, and the alternative hypothesis | . Hy :py =1y Hyp # 1y (b) Determine the type of test statistic to use. Degrees of freedom: 13 (c) Find the value of the test statistic. (Round to three or more decimal places.) 2.750 (d) Find the two critical values at the 0.01 level of significance. (Round to three or more decimal places.) ~ —3.012 and 3.012 Can we conclude that the mean cost per unit for plants using electricity differs from the mean cost per unit for plants using gas? (e ~ Yes No
