Question

The following data give the percentages of random samples of United Kingdom citizens who were smokers, in a variety of years.

  Age (years)

Year 16–19 20–24 25–34 35–49 50–59 60+

1978 34 44 45 45 45 30

1988    28 37 36 36 33 23

1998 31 40 35 30 27 16

2000 29 35 35 29 27 16

2002 25 38 34 28 26 15

2007 20 31 27 22 21 12

(a) Test the hypothesis that the actual percentages of smokers do not depend on the year considered. (b) Test the hypothesis that there is no effect due to age group.

Answer 1

The following data give the percentages of random samples of United Kingdom citizens who were smokers, in a variety of years.

  Age (years)

Year 16–19 20–24 25–34 35–49 50–59 60+

1978 34 44 45 45 45 30

1988    28 37 36 36 33 23

1998 31 40 35 30 27 16

2000 29 35 35 29 27 16

2002 25 38 34 28 26 15

2007 20 31 27 22 21 12

(a) Test the hypothesis that the actual percentages of smokers do not depend on the year considered.

Calculated F= 34.55, P=0.000 which is < 0.05 level of significance. Ho is rejected. we conclude that actual percentages of smokers depend on the year considered.

(b) Test the hypothesis that there is no effect due to age group.

Calculated F= 41.43, P=0.000 which is < 0.05 level of significance. Ho is rejected. we conclude that there is an effect due to age group.

Excel Addon PHStat used

Randomized Block Design (ANOVA: Two-Factor Without Replication)
SUMMARY	Count	Sum	Average	Variance
y1978	6	243	40.5000	45.1000
y1988	6	193	32.1667	30.9667
y1998	6	179	29.8333	66.1667
y2000	6	171	28.5000	48.7000
y2002	6	166	27.6667	63.4667
y2007	6	133	22.1667	42.1667
16–19	6	167	27.8333	23.7667
20–24	6	225	37.5000	19.5000
25–34	6	212	35.3333	33.0667
35–49	6	190	31.6667	62.6667
50–59	6	179	29.8333	69.7667
60+	6	112	18.6667	43.8667
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
year	1103.4722	5	220.6944	34.5495	0.0000	2.6030
Age	1323.1389	5	264.6278	41.4272	0.0000	2.6030
Error	159.6944	25	6.3878
Total	2586.3056	35
				Level of significance		0.05