To test whether the mean time needed to mix a batch of material is the same for machines |produced by three manufacturers, the Jacobs Chemical Company obtained the following data on the time (in minutes) needed to mix the material. Use these data to conduct the hypotheses test about the different population mean times for mixing a batch of material for the three manufacturers. Make a conclusion. Use a = .05.

Manufacturer

M1 M2 M3
20 28 20
26 26 19
24 31 23
22 27 22

(EXAMPLE WITH SOLUTION)

Conde Nast Traveler conducts an annual survey in which readers rate their favorite cruise ships. Ratings are provided for small ships (carrying up to 500 passengers), medium ships carrying 500 to 1500 passengers), and large ships (carrying a minimum of 1500 passengers). The following data show the service ratings for eight randomly selected small ships, eight randomly selected medium ships, and eight randomly selected large ships. All ships are rated on a 100-point scale, with higher values indicating better service (Conde Nast Traveler, February 2003).

Use a = .05 to test for significant difference in the mean service ratings among the three sizes of cruise ships.

SOLUTION:

Results of using Excel's Anova: Single Factor Data Analysis tool:

1. Hypothesis Test.

are not all the same

2. Develop ANOVA table.

3. Use F-test to find p-value.

Please use ANOVA table for F and p-value
p = P(F ≥ 3.704) = .042.

4. Use rejection rule.
p-value 0.042 <α. It means not all population means are equal. Related to our problem we can make a conclusion:

5. Conclusion.