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  9  plants using electricity, which had a mean cost per unit of  $51.9  and standard deviation of  $7.98 , and  14  plants using gas, which had a mean of  $55.5  and standard deviation of  $8.73  . 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,  μ1 , differs from the mean cost per unit for plants using gas,  μ2 ? Perform a two-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. (If necessary, consult a list of formulas.)

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 7 plants using electricity, which had a mean cost per unit of $36.41 and standard deviation of $8.53, and 13 plants using gas, which had a mean of $46.50 and standard deviation of $8.60. 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 0.10 level of significance, that u, the mean cost per unit for plants using electricity, differs from H,, 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.)…

An analysis of variances produces dftotal = 16 and dfwithin = 14. For this analysis, how many treatment conditions are being compared?​

3. At a land farm, a farmer desired to test the effect of a given fertilizer on soybean production. He chose 24 plots of land of which are equal surface area. He treated 12 plots with the fertilizer and the others were untreated. Otherwise the conditions were the same. The treated plots produced soybean with mean yield 5.1 bushels and a standard deviation of 0.36 bushels, while the untreated plots had mean yield 4.8 bushels and a standard deviation of 0.40 bushels. (a) Can we conclude that there is a significant improvement in soybean production because of the fertilizer if a significance level of 1% is used? (b) What is the P-value of the test?