Question

Ch 13 Q1

Random sampling from four normally distributed populations produced the following data: (You may find it useful to reference the E Treatments -16 -10 -8-14-19 -10 -12 -15 14 -19 -16 DClick here for the Excel Data File a. Calculate the grand mean. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.) Grand mean b. Calculate SSTR and MSTR. (Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.) SSTR MSTR

Answer 1

X3 16 -10 19 9 16 X3 Total X2 10 12 -14 19 15 16 176 18 -6.0000 116 4.0000 Average Total-Ex EX/ni- 13.7500 801 14.9167 -14.0000 11.0000 437 37.0000 grand meangrand-11.7333 18.5000 Total observation number of groups 15 between groups degree of freedom dfn. -k-1 - within groups degree of freedom dfwg-N-k - Total degree of freedom dfrotal 14 -6.0000 13.7500 14.0000 11.0000 4.000 14.917 18.500 37.000 98.61 16.27 25.69 1.61 142.1833 8.00 44.75 74.00 74.00 200.7500 total sum of square between groups SSG 142.1833 200.7500 342.9333 sum of square within groups SSE total sum of square SSG+SSE Summary table Source of variation treatment error total 142.183 200.750 342.933 df 3.0000 11.0000 14.0000 MS 47.4 18.3 2.60

a)

Grand mean =-11.73

b)

SSTR=142.1833

MSTR=47.3944

c)

SSE=200.7500

MSE =18.2500

d)

Ho: $\mu$_A=$\mu$_B=$\mu$_C=$\mu$_D ; Ha: not all population means are equal

e-1)

test statistic F =2.597