12.47 How do women compare with men in their ability to perform laborious tasks that require strength?

Some information on this question is provided in a study by Phillips and Pepper of the fire-fighting ability of men and women. (“Shipboard Fire-

Fighting Performance of Females and Males,”

Human Factors, 1982). Phillips and Pepper conducted a factorial experiment to investigate the effect of the factor sex (male or female)

and the factor weight (light or heavy) on the length of time required for a person to perform a particular fire-fighting task. Eight persons were selected for each of the sex/weight categories of the factorial experiment, and the length of time needed to complete the task was recorded for each of the 32 persons. The means and standard deviations of the four samples are shown in table below.

a Calculate the total of the time measurements for each of the four categories of the factorial experiment.

b Use the result of part

(a) to calculate the sums of squares for sex, weight, and the sex/weight interaction.

2 * 2 n = 8 Light Heavy Mean Standard Deviation Mean Standard Deviation Female 18.30 6.81 14.50 2.93 Male 13.00 5.04 12.25 5.70 2 * 2 2 * 2 = 4 c Calculate each sample variance. Then calculate the sum of squares of deviations within each sample for each of the four samples.
d Calculate SSE. [Hint: SSE is the pooled sum of squares of the deviations calculated in part (c).]
e Now that you know SS(Sex), SS(Weight), SS(Sex Weight), and SSE, find SS (Total).
f Summarize the calculations in an analysis of variance table.
g Explain the practical significance of the presence (or absence) of sex/weight interaction.
Do the data provide evidence of a sex/weight interaction?
h Do the data provide sufficient evidence to indicate a difference in time required to complete the task between light men and light women? Test by using .
i Do the data provide sufficient evidence to indicate a difference in time to complete the task between heavy men and heavy women?
Test by using .