Question

Previous studies suggest that vegetarians may not receive enough zinc in their diets. As the zinc requirement is particularly important during pregnancy, researchers conducted a study to determine whether vegetarian pregnant women are at greater risk from low zinc levels than are nonvegetarian pregnant women.

23 women were monitored. The following table presents the zinc levels (ug/g) in the hair of three groups of women. (Data from J. C. King. Nutrition 34 (1981): 1049-1055.)

Pregnant nonvegetarians	Pregnant vegetarians	Nonpregnant vegetarians
185	171	210
189	174	139
187	202	172
181	171	198
150	207	177
176	125
	189
	179
	163
	174
	184
	186

How many degrees of freedom for the Between Groups calculation?

How many degrees of freedom for the Within Groups calculation?

F =

Critical value of F =  (use alpha = 0.05)

Should you reject the null hypothesis?

Answer 1

The statistical software output for this problem is:

Analysis of Variance results:
Data stored in separate columns.

Column statistics

Column	n	Mean	Std. Dev.	Std. Error
Pregnant nonvegetarians	6	178	14.477569	5.9104427
Pregnant vegetarians	12	177.08333	20.8739	6.0257759
Nonpregnant vegetarians	5	179.2	27.270864	12.195901

ANOVA table

Source	DF	SS	MS	F-Stat	P-value
Columns	2	16.196377	8.0981884	0.018372161	0.9818
Error	20	8815.7167	440.78583
Total	22	8831.913

Hence,

Between group degrees of freedom = 2

Within group degrees of freedom = 20

F = 0.018

Critical F value = 3.49

Do not reject Ho