State the expression by which you construct a 1001 alpha co

State the expression by which you construct a 100(1 - alpha)% confidence interval estimate for the true effect of the j level of factor B in a three factor fixed effects factorial design, where factor A occurs at 1 levels, factor B occurs at J levels, factor C occurs at K levels, and each treatment combination is replicated L times (L > 1).

Solution

A I

B J

C K

Total = I+j+k

Prob for B = j/i+j+k

p = j/i+j+k

Variance for p = i(i+k)/(i+j+k)

Std dev = sq root of  i(i+k)/(i+j+k)

For confidence interval 100(1-alpha)% we have z alpha/2 for z

Margin of error = z alpha/2(sq root of  i(i+k)/(i+j+k)

Confidence interval = [ j/i+j+k-z alpha/2(sq root of  i(i+k)/(i+j+k),  j/i+j+k+sq root of  i(i+k)/(i+j+k)]