Question

An article describes an experiment in which several types of boxes were compared with respect to compression strength (lb). The table below presents the results of a single-factor ANOVA experiment involving I = 4 types of boxes. Type of Box Sample Mean Sample SD 1 Compression Strength (lb) 655.5 788.3 734.3 721.4 679.1 699.4 789.2 772.5 786.9 686.1 732.1 774.8 713.00 46.55 2 756.93 40.34 3 737.1 639.0 696.3 671.7717.2 727.1 698.07 37.20 4 535.1 628.7 542.4 559.0 586.9 520.0 562.02 39.87 Suppose that the compression strength observations on the fourth type of box had been 652.1, 745.7, 659.4, 676.0, 703.9, and 637.0 (obtained by adding 117 to each previous xaj). Assuming no change in the remaining observations, carry out an F test with a = 0.05. State the appropriate hypotheses. O Ho: M1 M2 * 3 * H4 Ha: all four 's are equal O Ho: M1 = 42 = M3 = 14 Ha: all four 's are unequal O Ho: H1 * 2 * 3 * M4 Ha: at least two u's are equal yes Ho: Mi = 2 = H3 = 44 Ha: at least two ui's are unequal correct b) Calculate the test statistic. (Round your answer to two decimal places.) f= 1230 wrong answer c) What can be said about the p-value for the test? O p-value > 0.100 O 0.050 < P-value < 0.100 O 0.010 < P-value < 0.050 O 0.001 < P-value < 0.010 P-value < 0.001 X wrong answer

Answer 1

Ho: Mi = H2 = M3 - M4 Ha: at least two wi's are unequal

b)

Applying one way ANOVA:

Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	19810.8046	3	6603.6015	3.9030	0.0240	3.0984
Within Groups	33838.9750	20	1691.9488
Total	53649.7796	23

f =3.90

c)

0.01 < p value <0.05