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 Compression Strength (lb) Sample Mean Sample SD 1 655.5 788.3 734.3 721.4 679.1 699.4 713.00 46.55 2 3 789.2 772.5 786.9 686.1 732.1 774.8 737.1 639.0 696.3 671.7 717.2 727.1 756.93 40.34 4 535.1 628.7 542.4 559.0 586.9 520.0 698.07 562.02 37.20 39.87 ЛUSE SALT Suppose that the compression strength observations on the fourth type of box had been 648.1, 741.7, 655.4, 672.0, 699.9, and 633.0 (obtained by adding 113 to each previous X4;). Assuming no change in the remaining observations, carry out an F test with α = 0.05. State the appropriate hypotheses. O Ho M₁ =μ₂ = μ3 = μ4 Ha at least two μ's are unequal Ho: M₁ = μ2 #M3 #μ4 H₂: all four μ's are equal O Ho M₁ = M2 = μ3 = μ4 Ha all four μ's are unequal # = O Ho: M1 M2 M3 & M4 Ha at least two μ's are equal Calculate the test statistic. (Round your answer to two decimal places.) f = 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 State the conclusion in the problem context. ○ Fail to reject Ho. There is a difference in compression strengths among the four box types. ○ Reject Ho. There is a difference in compression strengths among the four box types. ○ Reject Ho. There is not a difference in compression strengths among the four box types. ○ Fail to reject Ho. There is not a difference in compression strengths among the four box types.
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 Compression Strength (lb) Sample Mean Sample SD 1 655.5 788.3 734.3 721.4 679.1 699.4 713.00 46.55 2 3 789.2 772.5 786.9 686.1 732.1 774.8 737.1 639.0 696.3 671.7 717.2 727.1 756.93 40.34 4 535.1 628.7 542.4 559.0 586.9 520.0 698.07 562.02 37.20 39.87 ЛUSE SALT Suppose that the compression strength observations on the fourth type of box had been 648.1, 741.7, 655.4, 672.0, 699.9, and 633.0 (obtained by adding 113 to each previous X4;). Assuming no change in the remaining observations, carry out an F test with α = 0.05. State the appropriate hypotheses. O Ho M₁ =μ₂ = μ3 = μ4 Ha at least two μ's are unequal Ho: M₁ = μ2 #M3 #μ4 H₂: all four μ's are equal O Ho M₁ = M2 = μ3 = μ4 Ha all four μ's are unequal # = O Ho: M1 M2 M3 & M4 Ha at least two μ's are equal Calculate the test statistic. (Round your answer to two decimal places.) f = 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 State the conclusion in the problem context. ○ Fail to reject Ho. There is a difference in compression strengths among the four box types. ○ Reject Ho. There is a difference in compression strengths among the four box types. ○ Reject Ho. There is not a difference in compression strengths among the four box types. ○ Fail to reject Ho. There is not a difference in compression strengths among the four box types.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 58E: What is meant by the sample space of an experiment?
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Transcribed Image Text: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
Compression Strength (lb)
Sample Mean Sample SD
1
655.5 788.3 734.3 721.4 679.1 699.4
713.00
46.55
2
3
789.2 772.5 786.9 686.1 732.1 774.8
737.1 639.0 696.3 671.7 717.2 727.1
756.93
40.34
4
535.1 628.7 542.4 559.0 586.9 520.0
698.07
562.02
37.20
39.87
ЛUSE SALT
Suppose that the compression strength observations on the fourth type of box had been 648.1, 741.7, 655.4, 672.0, 699.9, and 633.0 (obtained by adding 113 to each previous X4;). Assuming no change in the remaining observations, carry out an F test with α = 0.05.
State the appropriate hypotheses.
O Ho M₁ =μ₂ = μ3 = μ4
Ha at least two μ's are unequal
Ho: M₁ = μ2 #M3 #μ4
H₂:
all four μ's are equal
O Ho M₁ = M2 = μ3 = μ4
Ha all four μ's are unequal
#
=
O Ho: M1 M2 M3 & M4
Ha at least two μ's are equal
Calculate the test statistic. (Round your answer to two decimal places.)
f =
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
State the conclusion in the problem context.
○ Fail to reject Ho. There is a difference in compression strengths among the four box types.
○ Reject Ho. There is a difference in compression strengths among the four box types.
○ Reject Ho. There is not a difference in compression strengths among the four box types.
○ Fail to reject Ho. There is not a difference in compression strengths among the four box types.
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