Question

In: Statistics and Probability

An article described an experiment in which several different types of boxes were compared with respect...

An article described an experiment in which several different types of boxes were compared with respect to compression strength (in pounds). The data in the table below resulted from a single-factor experiment involving k = 4 types of boxes (the sample means and standard deviations are in close agreement with values given in the paper). Do these data provide evidence to support the claim that the mean compression strength is not the same for all four box types? Test the relevant hypothesis using a significance level of .01 if = 685.42. Type of Box Compression Strength (lb)

Sample Mean Sample SD

1 711.4 689.4 689.1 655.5 744.3 778.3 711.33 43.96

2 696.1 772.5 732.1 786.9 784.8 799.2 761.93 39.68

3 727.1 661.7 737.1 649.0 727.2 706.3 701.40 37.27

4 596.9 542.4 530.0 545.1 618.7 569.0 567.02 34.71

F = (Give the answer to one decimal place.)

PLEASE SHOW WORK SO I CAN LEARN HOW TO DO THIS :)

Expert Solution

Please note we have calculated mean and standard deviation again to verify the data given. Following are steps given to calculate value of F and test claim

SS_between = SS_total - SS_within = 155308.98 - 30505.975 = 124803.005

Based on above calculation:

Answer

F = 27.3 (Rounded to one decimal place)

There is enough evidence to support the claim that the mean compression strength is not the same for all four box types

orchestra answered 2 years ago

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