Please help Engineers are testing company fleet vehicle fuel economy (miles per gallon) performance by using different types of fuel. One vehicle of each size is tested. Does this sample provide sufficient evidence to conclude that there is a significant difference in treatment means?| | 87 Octane | 89 Octane | 91 Octane | Ethanol 5% | Ethanol 28% ||----------------|-----------|-----------|-----------|------------|-------------|| Compact | 31.9 | 28.0 | 29.7 | 27.3 | 29.3 || Mid-Size | 18.9 | 18.2 | 20.4 | 18.9 | 27.3 || Full-Size | 23.4 | 22.9 | 19.8 | 30.9 | 28.0 || SUV | 18.1 | 23.2 | 15.2 | 21.4 | 30.4 |[Click here for the Excel Data File](a) Choose the correct statement.- ☐ Fuel type is the blocking factor and vehicle size is the treatment. - ☐ Fuel type is the treatment and vehicle size is the blocking factor.(b) Fill in the boxes. (Round your SS values to 3 decimal places, F values to 2 decimal places, and other answers to 4 decimal places.)| Source | SS | df | MS | F | p-value ||---------------------|------|----|-----|----|---------|| Treatments (Fuel Type) | | | | | || Blocks (Vehicle Size) | | | | | || Error | | | | | || Total | | | | | | **Data Table: Summary of Fuel Types and Vehicle Sizes**This table presents data on various fuel types and vehicle sizes, including statistics such as the mean, sample size (\(n\)), and standard deviation for each category. The specific numbers are not provided in the table displayed.**Categories:**- Fuel Types: 87 Octane, 89 Octane, 91 Octane, Ethanol 5%, Ethanol 10%- Vehicle Sizes: Compact, Mid-Size, Full-Size, SUV- Total**Questions:****(c)** Choose the correct statement. Use \(\alpha = 0.05\).- \( \square \) Fuel type means differ significantly and vehicle size is also a significant factor.- \( \square \) Fuel type means do not differ significantly, but vehicle size is a significant factor.- \( \square \) Fuel type means differ significantly, but vehicle size is not a significant factor.- \( \square \) Fuel type means do not differ significantly and vehicle size is not a significant factor.**(d)** Which fuel types show a significant difference in average fuel economy? Use \(\alpha = 0.05\). (You may select more than one answer. Click the box with a check mark for the correct answer and click to empty the box for the wrong answer.)- \( \square \) Ethanol 10% and 87 Octane- \( \square \) Ethanol 5% and 89 Octane- \( \square \) 87 Octane and 91 Octane- \( \square \) Ethanol 10% and 91 OctanePlease note: There are no specific values provided for mean, sample size, or standard deviation in the image displayed.

Since you have posted a question with multiple sub-parts, we will solve first three subparts for you. To get remaining sub-part solved please repost the complete question and mention the sub-parts to be solved.(a) From the given information, the fuel type is treatment, and vehicle size is the blocking factor. Correct Answer: Fuel type is treatment and vehicle size is the blocking factor.(b) The ANOVA is obtained by using the EXCEL as follows: Enter the data. Select Data > Data Analysis >ANOVA: Two-Factor Without Replication> OK. Enter Input Range as A1:F5. Mark Labels. Enter Alpha as 0.05. Click OK. The output is, The Two-Factor ANOVA table is, Source SS df MS F p-value Treatments(Fuel Type) 191.273 4 47.8183 4.06 0.0261 Blocks (Vehicle Size) 190.122 3 63.3738 5.39 0.0140 Error 141.211 12 11.7676 Total 522.606 19 The mean, sample size, and standard deviation are, Group Mean n Standard Deviation 87 Octane 24.325 4 6.8840 89 Octane 24.6 4 4.9612 91 Octane 19.025 4 2.5773 Ethanol 5% 24.625 4 5.4683 Ethanol 10% 28.75 4 1.3772 Compact 27.44 5 4.1567 Mid-size 20.74 5 3.7541 Full-size 27.22 5 4.2944 SUV 21.66 5 5.7713 Total 24.265 20 5.2446(c) Decision rule: If the p-value is less than(or equal to) level of significance, then reject the null hypothesis and indicate that the means differ significantly. Conclusion: The both p-value are less than level of significance. Based on the decision rule, reject the null hypothesis. Therefore, fuel type and vehicle size means are differ significantly. Correct Answer: fuel type means differ significantly and vehicle size is also a significant factor.

Math

Statistics

Engineers are testing company fleet vehicle fuel economy (miles per gallon) performance by using different types of fuel. One vehicle of each size is tested. Does this sample provide sufficient evidence to conclude that there is a significant difference in treatment means? 87 Oetane 31.9 89 Octane 28.e 18.2 29.e 91 Octane Ethanol 5% Ethanol 18% Compact Mid-Size 20.7 27.3 29.3 27.3 18.9 20.4 18.9 Full-Size SUV 28.4 18.1 19.8 30.9 28.e 23.2 15.2 21.4 30.4 Click here for the Excel Data File (a) Choose the correct statement. O Fuel type is the blocking factor and vehicle size is the treatment. O Fuel type is the treatment and vehicle size is the blocking factor. (b) Fill in the boxes. (Round your SS values to 3 decimal places, Fvalues to 2 decimal places, and other answers to 4 decimal places.) Two-Factor ANOVA p-value Source df MS Treatments (Fuel Type) Blocks (Vehicle Size) Error Total