Question

The effects of detergent brand name (factor A in columns) and the temperature of the water (factor B in rows) on the brightness of washed fabrics are being studied. Four brand names and two temperature levels are used; six observations for each combination are examined. The following ANOVA table is produced.

ANOVA
Source of Variation	SS		df	MS	F	p-value
Sample	75		1	75	63.38	8.92E−10
Columns	130.25		3	43.42	36.69	1.45E−11
Interaction	8.67		3	2.89	2.44	0.078
Within	47.33		40	1.18
Total	261.25		47

a. Can you conclude that there is interaction between the detergent brand name and the temperature of the water at the 5% significance level?

• Yes, since the p-value associated with interaction is less than significance level.

• Yes, since the p-value associated with interaction is greater than significance level.

• No, since the p-value associated with interaction is less than significance level.

• No, since the p-value associated with interaction is greater than significance level.

b-1. Are you able to conduct tests based on the main effects?

• Yes

• No

b-2. If yes, conduct these tests at the 5% significance level. (You may select more than one answer. Single click the box with the question mark to produce a check mark for a correct answer and double click the box with the question mark to empty the box for a wrong answer. Any boxes left with a question mark will be automatically graded as incorrect.)

• Differences exist in the average brightness of fabrics depending on the detergent brand name.unanswered
• Differences do not exist in the average brightness of fabrics depending on the detergent brand name.unanswered
• Differences exist in the average brightness of fabrics depending on the temperature of the water.unanswered
• Differences do not exist in the average brightness of fabrics depending on the temperature of the water.unanswered

Answer 1