A random sample of 9 compact, 9 midsize, and 9 full size cars was obtained and t
ID: 3222485 • Letter: A
Question
A random sample of 9 compact, 9 midsize, and 9 full size cars was obtained and the combined city/highway mpg was recorded. The data are below. (http://www.socscistatistics.com/tests/anova/default2.Aspx) a. What is the factor? What is the response variable? b. Test to see if there is evidence fuel efficiency, as measured by combined city/highway mpg, is different, on average, depending on vehicle class? c. In terms of the problem, what is a type I error? d. In terms of the problem, what is a type II error? e. If there is a difference, which classes are different? f. Suppose one driver drove each compact car, a different driver drove each midsize car, and a third driver drove each full size car. i. What is wrong with this setup? ii. A possible fix is to use driver as a second factor. List the 9 treatments in this case and explain how many of each type of car should be in each treatment group?Explanation / Answer
Ans: The study is based on the Fuel Economy of the automobiles ie. the relationship between the distance traveled and fuel consumed.
a) The factor is the Size of the Car ( whether compact, mid size or full size) and the response variable is the Fuel Economy measured in terms of mpg ie. Miles Per Gallon.
c) Here the null hypothesis are that all the treament means are same ie. There is no significant difference in the size of the car and the alternative hypothesis is that there is significant difference among the treatment means.
By definition, rejection of the null hypothesis when it is true is said to be the so called Type 1 errors.
In terms of the problem, when we reject that the effect of all the treatments have same means when the actual condition is the same, we consider it as the type 1 error.
d) Consider the 1st part of the answer of the (c) part explained above, when we accept the null hypothesis when the alternative hypothesis is true is said to be Type 2 errors.
In terms of the problem, when we accept that the effect of treatment means are same when the actual condition is contrary is said to be the Type 2 error.
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