Question

An oil company wishes to study the effects of four different gasoline additives on mean gasoline mileage. The company randomly selects four groups of six automobiles each and assigns a group of six automobiles to each additive type (W, X, Y, and Z). Here all 24 automobiles employed in the experiment are the same make and model. Each of the six automobiles assigned to a gasoline additive is test driven using the appropriate additive, and the gasoline mileage for the test drive is recorded.

AutoSave Of H C l = LabAssignment2.xlsx - Read-Only - Ex... Search Sign in - o X Help Comments File 9 Share Data Analysis & Clear = - + LE Home Insert Page Layout Formulas Data Review View From Text/CSV De Recent Sources Queries & Connections Là Existing Connections Refresh B Properties From Table/Range All Edit Links Get & Transform Data Queries & Connections From Web Get Data Sort Reapply Filter Advanced Sort & Filter Text to Columns Es Data Tools What If Forecast Analysis Sheet Forecast il Group Ungroup 28 Subtotal Outline Analysis 115 : x foc f)3 A B C D E F Anova: Single Factor G H I J K L M N 1 x W Y Z 35.7 SUMMARY Groups Count Homoa 31.2 32.6 30.8 31.5 32 30.1 27.6 28.1 27.4 28.5 27.5 28.7 34 35.1 33.9 36.1 34.8 34.5 36.2 35.2 35.8 34.9 35.3 Sum Average Variance 188.2 31.3666667 0.77866667 167.8 27.9666667 0.30266667 209.6 34.9333333 0.78666667 211.9 35.3166667 0.37366667 6 9 b) completely randomized design df ANOVA Source of Variation Between Groups Within Groups SS 213.88125 11.2083333 MS P-value Fcrit 3 71.29375 127.215613 3.3886E-13 3.09839121 20 0.56041667 15 f) 3 Total 225.089583 23 19 h) Q1 Q2 € Edit EO - + 99% Type here to search O OO * Bow 1 x ?^. » 9715019 6

d) What is the test statistic?
e) What is the critical value?
f) What is the between treatment degrees of freedom?
g) What is the test result? (Reject Ho / Fail to reject Ho).
h) Interpret the result in the context.

Answer 1

Answer Date: 02/12/2019 To test the hypothesis is that there is a difference in mean gasoline mileage among four different gasoline additives at 5% level of significance. The null and alternative hypothesis is, Ho:fli = H2 = Hz = HA Ha: at least one y; is unequal. The F-test statistics is, From the Excel output, the F-test statistics is 127.2156). e) The F-critical value is,

From the Excel output, the F-critical value is 3.0984). The between treatment degrees of freedom are, Decision The F-test statistics is 127.2156 is greater than F-critical value which is 3.0984, the null hypothesis is rejected at 5% level of significance. h) There is sufficient evidence that there is a difference in mean gasoline mileage among four different gasoline additives. The result is statistically significant.