Question

1. Nerve growth factor (NGF) is a protein that has been shown to play a role in the development and maintenance of peripheral sympathetic neurons. Once approach to the study of NGF is to deprive the animal of NGF and study the effect of this deprivation on various cell types. In this study, the effect of the total protein content in the dorsal root ganglia of rats is considered. Two groups of rats are compared: those born to NGF-deficient females (in utero) and those born to normal females but nursed by NGF-deficient females (in milk). These data result:

Total protein content, milligrams of protein per dorsal root ganglion

In utero (U)                                           In milk (M)

.13     .09                                             .19     .20

.19     .13                                             .21     .22

.19     .21                                             .21

.20                                                       .23

Do these data indicate at the alpha = 0.05 level that the total protein content tends to be smaller among rats deprived of NGF in utero than among those deprived of the growth factor in milk? Complete the appropriate test.

data is non parametric

Answer 1

The hypothesis being tested is:

Null hypothesis	H₀: η₁ - η₂ = 0
Alternative hypothesis	H₁: η₁ - η₂ < 0

n	sum of ranks
7	33.5	U
6	57.5	M
13	91	total
	49.000	expected value
	7.000	standard deviation
	-2.214	z
	.0134	p-value (one-tailed, lower)

The p-value is 0.0134.

Since the p-value (0.0134) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the total protein content tends to be smaller among rats deprived of NGF in utero than among those deprived of the growth factor in milk.