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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 12 plants using electricity, which had a mean cost pe unit of $66.99 and standard deviation of $8.75, and 14 plants using gas, which had a mean of $58.50 and standard deviation of $8.46. 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 ₂, the mean cost per unit for plant 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 Ho and the alternative hypothesis H₁. H:0 H₁ :0 (b) Determine the type of test statistic to use. t Degrees of freedom: (c) Find the value of the test statistic. (Round to three or more decimal places.) 3 XI 5 a *O S 2 0=0 OSO

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 12 plants using electricity, which had a mean cost pe unit of $66.99 and standard deviation of $8.75, and 14 plants using gas, which had a mean of $58.50 and standard deviation of $8.46. 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 ₂, the mean cost per unit for plant 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 Ho and the alternative hypothesis H₁. H:0 H₁ :0 (b) Determine the type of test statistic to use. t Degrees of freedom: (c) Find the value of the test statistic. (Round to three or more decimal places.) 3 XI 5 a *O S 2 0=0 OSO

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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 12 plants using electricity, which had a mean cost per unit of $66.99 and standard deviation of $8.75, and 14 plants using gas, which had a mean of $58.50 and standard deviation of $8.46. 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 \(H_0\) and the alternative hypothesis \(H_1\). \(H_0 :\) \(H_1 :\) (b) Determine the type of test statistic to use. Type selected: t Degrees of freedom: (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) Explanation | Check 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy
Transcribed Image Text: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 12 plants using electricity, which had a mean cost per unit of $66.99 and standard deviation of $8.75, and 14 plants using gas, which had a mean of $58.50 and standard deviation of $8.46. 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 \(H_0\) and the alternative hypothesis \(H_1\). \(H_0 :\) \(H_1 :\) (b) Determine the type of test statistic to use. Type selected: t Degrees of freedom: (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) Explanation | Check 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy
### Statistical Hypothesis Testing This image provides a framework for conducting a statistical hypothesis test. Follow the steps below to determine whether the mean cost per unit for plants using electricity differs from the mean cost per unit for plants using gas. #### Steps: **(a) Formulate Hypotheses:** - **Null Hypothesis (\(H_0\))**: There is no difference in the mean cost per unit for plants using electricity versus gas. - **Alternative Hypothesis (\(H_1\))**: There is a difference in the mean cost per unit for plants using electricity versus gas. **(b) Select Test Statistic:** - Choose the appropriate test statistic, indicated here as "t" for a t-test. - Specify the **degrees of freedom**, which is crucial for determining the accurate critical value. **(c) Calculate Test Statistic:** - Compute the test statistic value based on sample data. - Ensure you round the result to three or more decimal places. **(d) Determine p-value:** - Find the p-value corresponding to the calculated test statistic. - Round the p-value to three or more decimal places for accuracy. **(e) Draw Conclusion:** - Based on the p-value and pre-determined significance level (often 0.05), decide whether we can conclude that the mean cost per unit for plants using electricity differs from those using gas. - Select "Yes" if there is sufficient evidence to reject the null hypothesis, otherwise select "No". ### Additional Elements: - A sidebar includes symbols and notations used in statistics, such as population mean (\(\mu\)), sample mean (\(\bar{x}\)), standard deviation (\(s\)), etc. This setup helps perform a comprehensive hypothesis test, crucial for determining differences in means across different treatments or conditions. Always ensure calculations are accurate for reliable results.
Transcribed Image Text:### Statistical Hypothesis Testing This image provides a framework for conducting a statistical hypothesis test. Follow the steps below to determine whether the mean cost per unit for plants using electricity differs from the mean cost per unit for plants using gas. #### Steps: **(a) Formulate Hypotheses:** - **Null Hypothesis (\(H_0\))**: There is no difference in the mean cost per unit for plants using electricity versus gas. - **Alternative Hypothesis (\(H_1\))**: There is a difference in the mean cost per unit for plants using electricity versus gas. **(b) Select Test Statistic:** - Choose the appropriate test statistic, indicated here as "t" for a t-test. - Specify the **degrees of freedom**, which is crucial for determining the accurate critical value. **(c) Calculate Test Statistic:** - Compute the test statistic value based on sample data. - Ensure you round the result to three or more decimal places. **(d) Determine p-value:** - Find the p-value corresponding to the calculated test statistic. - Round the p-value to three or more decimal places for accuracy. **(e) Draw Conclusion:** - Based on the p-value and pre-determined significance level (often 0.05), decide whether we can conclude that the mean cost per unit for plants using electricity differs from those using gas. - Select "Yes" if there is sufficient evidence to reject the null hypothesis, otherwise select "No". ### Additional Elements: - A sidebar includes symbols and notations used in statistics, such as population mean (\(\mu\)), sample mean (\(\bar{x}\)), standard deviation (\(s\)), etc. This setup helps perform a comprehensive hypothesis test, crucial for determining differences in means across different treatments or conditions. Always ensure calculations are accurate for reliable results.
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