An automobile dealer conducted a test to determine whether the time needed to complete a minor engine tune-up depends on whether a computerized engine analyzer or an electronic analyzer is used. Because tune-up time varies among compact, intermediate, and full-sized cars, the three types of cars were used as blocks in the experiment. The data (time in minutes) obtained follow. Car
Compact Intermediate Full Size
Analyzer Computerized 50 55 63
Electronic 42 44 46
The following regression model can be used to analyze the data for a randomized block design involving two treatments and three blocks.
E(y) = 0 + 1 x 1 + 2 x 2 + 3 x 3
a. Show the values of the variables below. If your answer is "zero" enter "0".
Analyzer x 1
Computerized ?
Electronic 1
Car x 2 x 3
Compact 0 0
Intermediate 1 ?
Full Size 0 ?
b. Enter negative values as negative number.
Show the estimated regression equation (to 1 decimal, if necessary).
y = + x 1 + x 2 + x 3
c. What is the value of the t test statistic for the type of analyzer (to 2 decimals)? Use α = .05 to test for any significant differences.
d. What is the p-value?
Select {less than .01, between .01 and .025, between .025 and .05, between .05 and .10, greater than .10,}I
What is your conclusion?
Select {Conclude that the mean time is different for the two types of analyzers, Cannot conclude that the type of analyzer has a significant effect on the mean time}