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 713.00 46.55 Compression Strength (lb) 655.5 788.3 734.3 721.4 679.1 699.4 789.2 772:5 786.9 686.1 732.1 774.8 737.1 639.0 696.3 671.7 717.2 727.1 2 756.93 40.34 3 698.07 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 X43). Assuming no change in the remaining observations, carry out an F test with a = 0.05. a) state the appropriate hypotheses. O Ho: 41 * M2 + 3 + 4 Ha: all four wi's are equal 3 d) State the conclusion in the problem context. O Fail to reject Ho. There is not a difference in compression strengths among the four box types. O Ho: Mi = 12 = H3 = 14 Ha: all four ui's are unequal Reject Ho. There is a difference in compression strengths among the four box types. O Fail to reject Ho. There is a difference in compression strengths among the four box types. O Ho: H1 H2 * 13 * H4 Ha: at least two u's are equal O Reject Ho. There is not a difference in compression strengths among the four box types. O Ho: Hi = H2 = M3 = 14 Ha: at least two y's are unequal You may need to use the appropriate table in the Arrendix of Tables to answer this question. b) Calculate the test statistic. (Round you f= Need Help? Read It Talk to a Tutor c) What can be said about the P-value for O p-value > 0.100 0.050 < P-value < 0.100 0 0.010 < P-value < 0.050 O 0.001 < P-value < 0.010 O p-value < 0.001

Answer 1

Sol:

perform ANOVA one way in excel

Install analysis tooplak in excel \

Go to

Data>Data analysis>ANOVA single factor we get

535.1 628.7 542.4 Anova: Single Factor 655.5 788.3 734.3 721.4 679.1 699.4 789.2 772.5 786.9 686.1 732.1 774.8 737.1 639 696.3 671.7 717.2 727.1 559 586.9 520 Input Range: $B$5:$E$11 Grouped By: O Columns O Rows Labels in First Row Alpha: 0.05

Output;

Anova: Single Factor Count Sum 6 SUMMARY Groups Type1 Type2 Type3 Type4 6 Average 4278 4541.6 4188.4 3372.1 Variance 713 2166.952 756.9333333 1626.947 698.0666667 1383.963 562.0166667 1589.934 6 6

ANOVA Source of Variation SS df Between Groups 127374.8 Within Groups 33838.97 MS 3 20 F P-value F crit 42458.25153 25.09429 5.53E-07 3.098391 1691.94875 Total 161213.7 23

ANSWER(A)

Ho:mu1=mu2=mu3=mu4

Ha:Atleast two Mui's are unequal

OPTION (D)

ANSWER(B)

F=25.09

ANSWER(C)

p value <0.001

ANSWER(D)

Reject Ho.There is a difference in compression strengths among the four box types.

OPTION B