Question

Are sexually active teenagers any better informed about AIDS and other potential health problems related to sex than teenagers who are sexually inactive? A 15-item test of general knowledge about sex and health was administered to random samples of teens who are sexually inactive, teens who are sexually active but with only a single partner, and teens who are sexually active with more than one partner. Is there any significant difference in the test scores? Inactive:10,12,8,10,8,5 active one partner: 11,11,6,5,15,10 active more than one partner 12,12,10,4,3,15

Please show computations without software.

Answer 1

The hypothesis being tested is:

H0: µ1 = µ2 = µ3

Ha: Not all means are equal

	Inactive	Active one	Active more
	10	11	12
	12	11	12
	8	6	10
	10	5	4
	8	15	3
	5	10	15
Mean, xi	8.833333	9.666667	9.333333
Variance, s²	5.766667	13.46667	23.06667
n	6	6	6
	xi	s²	n	n*(xi - xgrand)²	(n - 1)*s²
Inactive	8.833333	5.766667	6	1.185185	28.83333
Active one	9.666667	13.46667	6	0.907407	67.33333
Active more	9.333333	23.06667	6	0.018519	115.3333
Grand mean, xgrand	9.277778			SSB	SSE
				2.111111	211.5
Source	SS	df	MS	F	p-value
Between	2.111111	2	1.055556	0.074862	0.928216
Error	211.5	15	14.1
Total	213.6111	17

Source	SS	df	MS	F	p-value
Between	SSB	3 - 1	SS/df	MSB/MSE	Fdist(F,dfBetween,dfError)
Error	SSE	17 - 2	SS/df
Total	SSB+SSE	6 + 6 + 6 - 1

The p-value is 0.928216.

Since the p-value (0.928216) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we cannot conclude that there is any significant difference in the test scores.