A dendritic tree is a branched structure that emanates from the body of a nerve

Question

A dendritic tree is a branched structure that emanates from the body of a nerve cell. In a study of brain development, researchers examined brain tissue from 36 adult guinea pigs. The investigators randomly selected nerve cells from a certain region of the brain and counted the number of dendritic branch segments emanating from each selected cell. A total of 36 cells (1 per pig) was selected, and the resulting counts were as follows:
measurements
28 24 38 25
42 26 29 45
25 26 49 28
35 47 26 31
35 28 41 46
33 24 26 32
48 35 35 39
53 38 38 59
17 26 44 53

Perform a hypothesis test to address the questions. Define the Ho and Ha, compute the test statistic, define the reject region, estimate the p-value and then state the conclusion.

a) Is the mean number of cells is different from 37?
b) Is the mean number of cells is greater than 38?

Explanation / Answer

Using excel average and STDEVP functions

we find

population mean = 35.38889

standard deviation = 9.936682

a)

Hypothesis:

Ho: u!=37

Ha: u=37

test static:

Z = X-u/std/sqrt(n)

= 35.38889 - 37/ 9.936682/sqrt(36)

= -0.97283

Critical values:

at 0.5 level of significance
the critical values are -1.96 and +1.96

P-value:

from normal distribution table

P- value = 1.6694

conclusion :

when test static is greater than -1.96 and less than 1.96 , we reject null hypothesis

since test static is greater than -1.96 and less than 1.96 , we reject null hypothesis

so, there is not enough evidence that mean number of cells different from 37

b)

Hypothesis:

Ho: u!=38

Ha: u=38

test static:

Z = X-u/std/sqrt(n)

= 35.38889 - 38/ 9.936682/sqrt(36)

= -1.57665

Critical values:

at 0.5 level of significance
the critical values are -1.96 and +1.96

P-value:

from normal distribution table

P- value = 1.8851

conclusion :

when test static is greater than -1.96 and less than 1.96 , we reject null hypothesis

since test static is greater than -1.96 and less than 1.96 , we reject null hypothesis

so, there is not enough evidence that mean number of cells different from 38

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