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 14 plants using electricity, which had a mean cost per unit of $55.06 and standard deviation of $8.25, and 12 plants using gas, which had a mean of $57.80 and standard deviation of $7.81. 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 μ₁, the mean cost per unit for plants using electricity, differs from μ₂, 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 H and the alternative hypothesis H₁. HO H₁:0 (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Can we conclude that the mean cost per unit for plants using electricity differs from the mean cost per unit for plants using gas? Yes No I X 4 00 O X S 0=0 OSO 00 O>O G Р O

Researchers conducted an experiment to test the effects of alcohol. Errors were recorded in a test of visual and motor skills for a treatment group of 28 people who drank ethanol and another group of 28 people given a placebo. The errors for the treatment group have a standard deviation of 2.20, and the errors for the placebo group have a standard deviation of 0.77. Assume that the two populations are normally distributed. Use a 0.05 significance level to test the claim that both groups have the same amount of variation among the errors. Let sample 1 be the sample with the larger sample variance, and let sample 2 be the sample with the smaller sample variance. What are the null and alternative hypotheses? OB. Ho: 0=02 O A. H₁: 0²12 = 0²/2 H₁:0² > 0²/2 H₁:0² <0² O C. Ho: 0²/02/ H₁:0² = 0² Identify the test statistic. (Round to two decimal places as needed.) Use technology to identify the P-value. (Round to three decimal places as needed.) What is the conclusion for this hypothesis test?…

Research has shown that, for baseball players, good hip range of motion results in improved performance and decreased body stress. A research article reported on a study of independent samples of 40 professional pitchers and 40 professional position players. For the pitchers, the sample mean hip range of motion was 75.8 degrees and the sample standard deviation was 5.6 degrees, whereas the sample mean and sample standard deviation for position players were 79.9 degrees and 7.2 degrees, respectively. Assuming that the two samples are representative of professional baseball pitchers and position players, test hypotheses appropriate for determining if there is convincing evidence that the mean range of motion for pitchers is less than the mean for position players. (Use  ? = 0.05.  Use ?1 for pitchers and ?2 for position players.)

K.Brew sells a wide variety of outdoor equipment and clothing.  The company sells both through mail order and via the internet.  Random samples of sales receipts were studied for mail order sales and internet sales, with the total purchase being recorded for each sale.  A random sample of 18 sales receipts for mail order sales results in a mean sale amount of $81.30 with a standard deviation of $16.25 .  A random sample of 9 sales receipts for internet sales results in a mean sale amount of $67.00 with a standard deviation of $15.25 .  Using this data, find the 98% confidence interval for the true mean difference between the mean amount of mail order purchases and the mean amount of internet purchases.  Assume that the population variances are not equal and that the two populations are normally distributed. Step 2 of 3 :  Find the standard error of the sampling distribution to be used in constructing the confidence interval. Round your answer to two decimal places.