Question

Children are tested to determine their problem solving skills at three different ages (6, 8 and 10 years old). The scores on their problem solving tasks are given below. What conclusions can be drawn? The obtained statistic: 54.776

6 year olds 25 30 29 40 33 36 42 39

8 year olds 65 70 42 45 56 62 49 55

10 year olds 70 85 76 65 69 72 81 78

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

ANOVA test should be used.

The hypothesis being tested is:

H0: µ1 = µ2 = µ3

Ha: Not all means are equal

The critical value is 3.47.

	Mean	n	Std. Dev
	34.3	8	5.99	6 year olds
	55.5	8	9.84	8 year olds
	74.5	8	6.70	10 year olds
	54.8	24	18.33	Total
ANOVA table
Source	SS	df	MS	F	p-value	F-critical
Treatment	6,487.00	2	3,243.500	54.78	4.65E-09	3.47
Error	1,243.50	21	59.214
Total	7,730.50	23

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.