Laundry Detergent Preference Narrative
A consumer would like to know if there is a difference in the performance of three different laundry detergents. Eighteen pieces of white cloth were soiled with grape juice then washed in one of the three detergents A, B, or C. The resulting whiteness readings are listed below, where the larger number indicates whiter fabric.
-Refer to Laundry Detergent Preference Narrative. Calculate the value of the test statistic F.

Question

Laundry Detergent Preference Narrative
A consumer would like to know if there is a difference in the performance of three different laundry detergents. Eighteen pieces of white cloth were soiled with grape juice then washed in one of the three detergents A, B, or C. The resulting whiteness readings are listed below, where the larger number indicates whiter fabric. 
-Refer to Laundry Detergent Preference Narrative. Calculate the value of the test statistic F.

Quizplus · Accepted Answer

The Answer is

= 102,985,

= 1,357,

= 463,

= 411, and

= 483. The correction for the mean is CM =

=

/18 = 102,302.722. Then, Total SS =

= 102,985 - 102,302.722 = 682.278. SST =

= 102,763.1667 - 102,302.722 = 460.445. MST = SST/(k - 1) = 460.445/2 = 230.223. SSE = Total SS - SST = 682.278 - 460.445 = 221.833. MSE = SSE/(n - k) = 221.833/15 = 14.789. The value of the test statistic is F = MST/MSE = 230.223/14.789 = 15.567.