Question

A researcher is interested in determining the affect that prolonged practice has on a mouse's ability to sustain and use information that it has learned. He trains 18 mice on a laboratory maze. Each mouse runs the maze twice per day for two weeks. At the end of this initial training period the mice are randomly separated into three groups. The first group continues to run the maze twice per day for another week. The second group runs a brand new maze twice per day for one week. Mice from the third group remain in their home cage for the week, running no mazes. At the end of the week all mice are tested on their ability to complete the first maze. Each mouse runs the maze once and its time (in seconds) is recorded below. Determine if there are significant effects of the treatments. The obtained statistic: 4.87

Group One 10 12 18 15 16 12

Group Two 25 22 27 30 28 25

Group Three 15 17 20 21 19 18

What type of test should you use?

b. Please provide, in words, the null and alternative hypotheses.

c. Using an alpha level of .05 identify the critical value(s).

d. Using the above test statistic, alpha level and critical value(s) what is your statistical decision?

e. State your conclusion regarding the results from this test in language that a friend of yours with no knowledge of statistics could understand

Answer 1

One-Way ANOVA test

The hypothesis being tested is:

H0: µ1 = µ2 = µ3

Ha: Not all means are equal

The critical value is 3.68.

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that not all means are equal.

Group One	Group Two	Group Three
10	25	15
12	22	17
18	27	20
15	30	21
16	28	19
12	25	18
	Mean	n	Std. Dev
	13.8	6	2.99	Group One
	26.2	6	2.79	Group Two
	18.3	6	2.16	Group Three
	19.4	18	5.81	Total
ANOVA table
Source	SS	df	MS	F	p-value	F critical
Treatment	467.44	2	233.722	32.76	3.36E-06	3.68
Error	107.00	15	7.133
Total	574.44	17