Finding error variance and confidence interval Two new types of petrol, called premium and super, are introduced in the market, and their manufacturers claim that they give extra mileage. Following data were obtained on extra mileage which is defined as actual mileage minus 10. Data on Extra Mileage Ordinary Petrol 1 2 2 1 Premium Petrol 2 2 1 3 Super Petrol 4 1 2 3 (i) Using ANOVA, test whether premium or super gives an extra mileage. (ii) What is your estimate for the error variance? (iii) Assuming that the error variance is known and is equal to 1, obtain the 95 % confidence interval for the mean extra mileage of super.

Since this is homework, I am not going to give you and answer, but I will offer some suggestions that should help you in the right direction (including, I would hope, asking your teacher about things you don't understand):

1. This is a one-way ANOVA with Extra Mileage as the Factor and Fuel Type as the Treatment (it has three levels: Ordinary, Premium, Super).
2. Although the sample sizes are very small (and bounded to be positive), you are probably expected to assume the Extra mileage follows a normal distribution, with the mean being different for each treatment, but the variability being identitical for each fuel type.
3. Take a look at this link for the formulas to answer your questions