Mi Lang Motors has in stock three cars of the same make and model. The president would like to compare the gas consumption of the three cars (labeled car A, car B, and car C) using four different types of gasoline. For each trial, a gallon of gasoline was added to an empty tank, and the car was driven until it ran out of gas. The following table shows the number of miles driven in each trial.
Types of Gasoline Distance (miles)
Car A Car B Car C
Regular 22.4 20.8 21.5
Super regular 17.0 19.4 20.7
Unleaded 19.2 20.2 21.2
Premium unleaded 20.3 18.6 20.4
Using the .05 level of significance:
a. Is there a difference among types of gasoline?
b. Is there a difference in the cars?
If you thought you were doing a "cut and paste" it will not work here. You must type everything out.
Sra
To determine if there is a difference among the types of gasoline and a difference in the cars, we can perform a statistical analysis called a one-way analysis of variance (ANOVA). This analysis allows us to compare the means of multiple groups.
a. To test if there is a difference among types of gasoline, we would perform a one-way ANOVA on the data for each car. This will help us determine if there is a significant difference in gas consumption between the different types of gasoline.
b. To test if there is a difference in the cars, we would also perform a one-way ANOVA on the data for each type of gasoline. This analysis will help us determine if there is a significant difference in gas consumption between the cars.
Here's how you can perform an ANOVA analysis using statistical software such as R or Excel:
1. Input the data into a spreadsheet or statistical software. Create a table with the types of gasoline as the rows and the distances for each car as the columns.
2. Calculate the means for each group (car and gasoline type) and record them.
3. Calculate the overall mean by summing up all the distances and dividing by the total number of observations.
4. Calculate the sum of squares between groups (SSB) by summing up the squared differences between the group means and the overall mean, multiplied by the number of observations in each group.
5. Calculate the sum of squares within groups (SSW) by summing up the squared differences between each individual observation and its group mean, across all groups.
6. Calculate the degrees of freedom for SSB and SSW. The degrees of freedom for SSB is the number of groups minus 1, and the degrees of freedom for SSW is the total number of observations minus the number of groups.
7. Calculate the mean square between (MSB) by dividing the SSB by its degrees of freedom, and calculate the mean square within (MSW) by dividing the SSW by its degrees of freedom.
8. Calculate the F-value by dividing the MSB by the MSW.
9. Look up the critical F-value for your desired level of significance (in this case, 0.05) and compare it to the calculated F-value. If the calculated F-value is greater than the critical F-value, then you can reject the null hypothesis and conclude that there is a significant difference among the groups.
10. If the null hypothesis is rejected, you can perform post-hoc tests (such as Tukey's HSD test or Bonferroni correction) to determine which specific groups differ significantly from each other.
By following these steps and performing the analysis, you can determine if there is a difference among types of gasoline (a) and if there is a difference in the cars (b) in terms of gas consumption.