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5. 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 $56.40 and standard deviation of $8.13, and 12 plants using gas, which had a mean of $53.90 and standard deviation of $8.63. 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 the mean cost per unit for plants using electricity, /1, is greater than the mean cost per unit for plants using gas, Hz? Perform a test of the following hypotheses by answering parts a - c below. [9 points] Ho: M1 S H2 H1:141 > HZ a. Compute the value of the test statistic. Show work. Round to three decimal places if needed. b. Identify any critical values and shade the critical region(s). Using the critical value method, should Ho be rejected at the 0.01 level? C. Choose an appropriate conclusion based on your decision in part c. Circle your choice. 1. The mean cost per unit for plants using electricity is greater than the mean cost per unit for plants using gas. ii. There is not enough evidence to conclude that the mean cost per unit for plants using electricity is greater than the mean cost per unit for plants using gas