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 2 789.2 772.5 786.9 686.1 732.1 774.8 756.93 40.34 3 4 737.1 639.0 696.3 671.7 717.2 727.1 535.1 628.7 542.4 559.0 586.9 520.0 698.07 562.02 37.20 39.87 USE SALT Suppose that the compression strength observations on the fourth type of box had been 645.1, 738.7, 652.4, 669.0, 696.9, and 630.0 (obtained by adding 110 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 H0 μ₁ = μ₂ = μ3 = μ4 Ha at least two μ's are unequal O Ho: M₁ = μ₂ #M3 # M4 Ha at least two μs are equal Ho M1 M2 M3 = μ4 Ha all four μi's are unequal # Ho: M1 M2 M3 & M4 Ha: all four 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? ○ P-value > 0.100 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 not a difference in compression strengths among the four box types. Reject Ho. There is a difference in compression strengths among the four box types. Fail to 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.
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 2 789.2 772.5 786.9 686.1 732.1 774.8 756.93 40.34 3 4 737.1 639.0 696.3 671.7 717.2 727.1 535.1 628.7 542.4 559.0 586.9 520.0 698.07 562.02 37.20 39.87 USE SALT Suppose that the compression strength observations on the fourth type of box had been 645.1, 738.7, 652.4, 669.0, 696.9, and 630.0 (obtained by adding 110 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 H0 μ₁ = μ₂ = μ3 = μ4 Ha at least two μ's are unequal O Ho: M₁ = μ₂ #M3 # M4 Ha at least two μs are equal Ho M1 M2 M3 = μ4 Ha all four μi's are unequal # Ho: M1 M2 M3 & M4 Ha: all four 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? ○ P-value > 0.100 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 not a difference in compression strengths among the four box types. Reject Ho. There is a difference in compression strengths among the four box types. Fail to 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.
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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Question
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
789.2 772.5 786.9 686.1 732.1 774.8
756.93
40.34
3
4
737.1 639.0 696.3 671.7 717.2 727.1
535.1 628.7 542.4 559.0 586.9 520.0
698.07
562.02
37.20
39.87
USE SALT
Suppose that the compression strength observations on the fourth type of box had been 645.1, 738.7, 652.4, 669.0, 696.9, and 630.0 (obtained by adding 110 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 H0 μ₁ = μ₂ = μ3 = μ4
Ha at least two μ's are unequal
O Ho: M₁ = μ₂ #M3 # M4
Ha at least two μs are equal
Ho M1 M2 M3 = μ4
Ha
all four μi's are unequal
#
Ho: M1 M2 M3 & M4
Ha: all four 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?
○ P-value > 0.100
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 not a difference in compression strengths among the four box types.
Reject Ho. There is a difference in compression strengths among the four box types.
Fail to 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.
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