Question

A company manufactures printers and fax machines at plants located in Atlanta, Dallas, and Seattle. To measure how much employees at these plants know about quality management, a random sample of 6 employees was selected from each plant and the employees selected were given a quality awareness examination. The examination scores for these 18 employees are shown in the following table. The sample means, sample variances, and sample standard deviations for each group are also provided. Managers want to use these data to test the hypothesis that the mean examination score is the same for all three plants.

	Plant 1 Atlanta	Plant 2 Dallas	Plant 3 Seattle
	85	72	60
	74	75	63
	81	72	62
	75	73	69
	70	68	76
	89	84	66
Sample mean	79	74	66
Sample variance	52.4	29.2	34.0
Sample standard deviation	7.24	5.40	5.83

Set up the ANOVA table for these data. (Round your values for MSE and F to two decimal places, and your p-value to four decimal places.)

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
Treatments	?	?	?	?	?
Error	?	?	?
Total	?	?

Test for any significant difference in the mean examination score for the three plants. Use

α = 0.05.

Find the value of the test statistic. (Round your answer to two decimal places.)

_____________.

Find the p-value. (Round your answer to four decimal places.)

p-value = _________.

Answer 1

Ans:

df(treatments)=3-1=2

df(error)=18-3=15

Source	Sum	Degrees	Mean	F	p-value
of Variation	of Squares	of Freedom	Square
Treatments	516	2	258	6.70	0.0084
Error	578	15	38.53
Total	1094	17

Test statistic:

F=258/38.53=6.70

p-value=FDIST(6.70,2,15)=0.0084