Question

Suppose you are a researcher investigating the annual sales differences among five categories of businesses. The study looks at 55 companies equally divided among categories A, B, C, D, and E. Complete the following ANOVA table and determine the value of the F statistic. Could you help me find the p value and T? Treatment SS=583.39 and the total is 1555.57. The question Is on Chegg already but nobody has answered for the P and T values.

Answer 1

Solution:

Given:

N = total observations= 55

k = Number of business categories = 5

SSTr = 583.39

SST = 1555.57

Thus we use following steps to get F test statistic , P-value and T value.

df_treatments = k - 1

df_treatments = 5 - 1

df_treatments = 4

df_error  = N - k

df_error  = 55 - 5

df_error  = 50

df_total  = N -1

df_total  = 55 - 1

df_total  = 54

SSE = SST - SSTr

SSE = 1555.57 - 583.39

SSE = 972.18

Thus

MSTr = SSTr / df_treatments

MSTr = 583.39 / 4

MSTr = 145.8475

MSE = SSE /df_error  

MSE =  972.18 / 50

MSE = 19.4436

Thus

F = MSTr / MSE

F = 145.8475 / 19.4436

F = 7.501

To get exact P-value , we need to use Excel command:

=F.DIST.RT(F , df_treatments , df_error  )

=F.DIST.RT(7.501,4,50)

= 0.0000817

=  0.0001

( Rounded to 4 decimal places.)

We can find p-value interval using F table:

Look in F table for df_numerator = df_treatments = 4 and df_denominator = df_error = 50, Find F value interval in which F = 7.501 fall.

Then find corresponding right tail area interval. that would be P-value interval.

F = 7.501 > F = 5.46,

Right tail area for F = 5.46 is 0.001

then Right tail area for F = 7.501 < 0.001

Thus we get: P-value < 0.001

Source	SS	DF	MS	F	P-value
Treatments	583.39	4	145.8475	7.501	0.00008
Error	972.18	50	19.4436
Total	1555.57	54

To find T value we use following formula:

then