A study was conducted to determine if differences in new statistics textbook pri

Question

A study was conducted to determine if differences in new statistics textbook prices exist between on-campus bookstores, off-campus bookstores, and Internet bookstores. The study randomly selected 12 statistics textbooks and recorded the price of the textbooks for each of the outlets (hence, a total sample size of 36). The following information is provided:

SSA = 16,626.4

SSTotal = 17,477.6

At 0.01 level of significance, can we conclude that there is a difference in textbook prices across the three different outlets? Show all the steps of the hypothesis testing.

Explanation / Answer

null hypothesis:Ho: mean of all textbook prices across the three different outlets are same

alternate hypothesis:Ha: mean of at least 2 textbook prices across the three different outlets are different.

here SSA=16626.4

SST =17477.6

therefore SSE =SST-SSA =17477.6-16626.4=851.2

degree of freedom total=36-1=35

degree of freedom between treatments=number of outlets-1=3-1=2

degree of freedoms within=35-2=33

therefore mean square between treatments MSA=SSA/degree of freedom=16626.4/2=8313.2

mean square with in treatment MSE=SSE/degree of freedom =851.2/33=25.794

hence F dist =MSA/MSE =322.293

hence

from above p value =0.0000

as p value is less then 0.01 level of significance; we reject null hypothesis.

we can conclude that there is a difference in textbook prices across the three different outlets

please revert for any clarification

Source of variation SS df MS F P value F crit Between groups 16626.400 2 8313.200 322.293 0.00000 3.28492 with in groups 851.200 33 25.794 total 17477.600 35

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