A manufacturing researcher wants to determine if age or gender significantly affects the time required to learn an assembly line task. He randomly selected 24 adults aged 20 to 64 years old, of whom 8 are 20 to 34 years old (4 male, 4 female), 8 are 35 to 49 years old (4 male, 4 female), and 8 are 50 to 64 years old (4 male, 4 female). He then measured the time (in minutes) required to complete a certain task. The data obtained are shown next.

(a) The learning times are approximately normally distributed. Verify the requirement of equal population variances.

(b) Determine whether there is significant interaction between age and gender.

(c) If there is not significant interaction, determine whether or not there is significant difference in the means for the three age groups

(d) Draw an interaction plot of the data to support the results of parts (b) and (c).

(e) If there is significant difference in the means for the three age groups, use Tukey’s test to determine which pairwise means differ using a familywise error rate of a = 0.05.

Transcribed Image Text:

Gender Age (years) 20–34 5.2,5.1 5.7,6.1 5.3, 5.5 35-49 4.8, 5.8 5.0, 4.8 5.0, 5.4 5.6, 5.1 50-64 5.2, 4.3 5.5, 4.7 4.9, 5.5 Male Female 4.9, 5.6 5.5, 5.0