An automobile dealer conducted a test to determine if the...

An automobile dealer conducted a test to determine if the time in minutes 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 obtained follow. Analyzer Computerized Electronic Compact 49 42 Intermediate 57 45 Full-sized 62 45 Use $alpha = .05$ to test for any significant differences. Source Sum of Squares Degrees Mean Square $F$ $p$-value of Variation (to whole number) of Freedom (to 1 decimal) (to 2 decimals) (to 4 decimals) Treatments Blocks Error Total The $p$-value is - Select your answer - What is your conclusion? - Select your answer - that the mean tune-up times are not the same for both analyzers.

Transcript

00:01 Here in the problem we have given, given that is three types of cars.

00:06 We have three types of cars given and we have that is here number of, number of blocks that is b is equal to three.

00:22 And we have number of number of groups groups that is equal to g is equal to and we have alpha value is equal to point zero five now i will have the hypothesis stated it's not where we will have new new will be equal to that is new computerized let me write new computerized equal to electronic electronic that is new computerized it will be equal to the new year we will have electronic electronic and i will have x one that is the alternative hypothesis it is being represented as it is new we will have computerized that is computerized it should not be work with that is mute here electronic now this is the our hypothesis test cases now let me construct the construct that is an or table that is anova table for the given data so i will have that is here i will have i will have to just calculate sst okay and we will have to calculate ssb b and then we will have this value will be equal to summation of x square minus summation of x whole square divided by that is here b into g so from here i will have its value will be equal to that is 2 1 6 after calculating here b and g is that is as i already calculated here that is b and g value given here.

02:06 Now, similarly, i will have ssb value also.

02:09 So i will have here ssb, which will be equal to that is here summation of that is t i square upon b minus here i will have summation of x whole square upon that is b into g to it value after calculation will be equal to that is three zero seven nine nine nine three.

02:35 So this value we are getting now let me calculate the degree of freedom here.

02:39 So after this i will have that is degree of degree of freedom it will be equal to that is here i will have that is one is here g minus one that is the f of that is tr so it would be equal to b minus one that is g minus 1 let me write this is here g minus 1 now g minus 1 which is equal to 1 and i will have it is gf of that is block so it will be equal to b minus 1 which is equal to that is 2 now we will have that is df of that is the area of freedom of error df of e will be equal to that is is here df of the r into the df of b, which will be equal to two here.

03:30 Now these values we got after this, i just convert to the whatever.

03:34 So before calculating, i will just calculate ms ms, the r which is equal to that is ss, the r divided by here, that is df, df, er...

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