Question

.A researcher is interested in comparing sunblocks and their protection level for various skin types. He designed a two-factor factorial design with Factor A as type of sunblock with 4 levels and Factor B as skin type with 5 levels. He used 4 replications for each treatment. The protection level was measured on a scale from 1 to 5 based on the overall amount of sunburn for a 8 square centimeter patch of skin on the subjects' backs. Based on the researcher's design, how many total degrees of freedom are there for this experiment?

How many degrees of freedom are associated with the error for this experiment?

The SST was found to be 386.4 and the MSE was found to be 4.78. Compute the value of the F test statistic for the treatments.

Find the appropriate critical value for the hypothesis test for Factor B using an alpha of 0.05.

The results of a two-factor factorial experiment are shown in the table below:

Levels of Factor B : 1, 2

Levels of Factor A: A, B

A1: 8, 7

A2: 11, 13

B1: 10, 12

B2: 6, 5

Compute the SSA for this experiment

Answer 1

Based on the researcher's design, how many total degrees of freedom are there for this experiment?

(4-1) + (5-1) + 3*4 + 60 - 1= 79

How many degrees of freedom are associated with the error for this experiment?

60

The SST was found to be 386.4 and the MSE was found to be 4.78. Compute the value of the F test statistic for the treatments.

Not possible from this data.

Find the appropriate critical value for the hypothesis test for Factor B using an alpha of 0.05.

The critical value is 2.525.