An article describes an experiment in which several types of boxes were compared

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.

Suppose that the compression strength observations on the fourth type of box had been 735.1, 828.7, 742.4, 759.0, 786.9, 720.0 (obtained by adding 200 to each previous x4j). Assuming no change in the remaining observations, carry out an F test with = .05. (Give Fto 2 decimal places and the p-value to 3 decimal places.)

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 3 737.1 639.0 696.3 671.7 717.2 727.1 698.07 37.20 4 535.1 628.7 542.4 559.0 586.9 520.0 562.02 39.87 An article dascribes an axperimant in which several types of boxas were compared with respect to comprassicn strength (Ib). Tha tabla belaw presents the rasults of asingle-factor ANOVA axperimant involving -4 typcs of boxas. Iype of Box Compression Strength (lb) Sample Mean Sample sU /13.00 756.93 3 37.1 39.0 696. 71.7717.2 727.1.07 /y8.3 734.3 721.479.1 99.4 789. 7725 786.6.1 73 774.8 40.34 435.1 628.7 5424 550.0 586.9520.0 562.02 30.87 Suppose na he compress un re h u servati ris Un he fourU1 yp of bu had been 735.1 828.7 742 to 2 dedmal placas nd the P-value to 3 decimal place 759.0 786.9, 720. ub dr ed by dduru 200 u edch previou Assumin no chdnue n hererldininy u serva uns carry uu dn F esL with = 05 (G ve F -statistic = P-value =

Explanation / Answer

Result:

Suppose that the compression strength observations on the fourth type of box had been 735.1, 828.7, 742.4, 759.0, 786.9, 720.0 (obtained by adding 200 to each previous x4j). Assuming no change in the remaining observations, carry out an F test with = .05. (Give Fto 2 decimal places and the p-value to 3 decimal places.)

F-statistic

=3.59

P-value

= 0.032

One factor ANOVA

Mean

n

Std. Dev

Box1

713.00

6

46.551

Box2

756.93

6

40.335

Box3

698.07

6

37.202

Box4

762.02

6

39.874

Total

732.50

24

47.569

ANOVA table

Source

SS

   df

MS

F

   p-value

Treatment

18,204.755

3

6,068.2515

3.59

.0319

Error

33,838.975

20

1,691.9488

Total

52,043.730

23

F-statistic

=3.59

P-value

= 0.032

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