Question

A veterinary anatomist measured the density of nerve cells at a specified site in the intestine of fourteen horses. Each density value is the average of counts of nerve cells in five equal sections of tissue. 8.5 11.2 14.2 17.0 18.6 19.0 23.2 28.4 35.0 35.0 36.1 38.5 42.3 45.7 Use the sign test to determine if there is sufficient evidence that the median nerve cell density at this site is different from 35 [alpha = 0.10]

Answer 1

The sign test for the median nerve cell density is performed in the following steps,

Step 1:

Sort the data values from the smallest to the largest.

Step 2:

Assign positive signs for the value larger than 35 and -ve sign for the values smaller than 35. And count the number +ve and negative sign.

nerve cells	sign
8.5	-ve
11.2	-ve
14.2	-ve
17	-ve
18.6	-ve
19	-ve
23.2	-ve
28.4	-ve
35	-ve
35	-ve
36.1	+ve
38.5	+ve
42.3	+ve
45.7	+ve

Number of positive = 4

Number of negative = 10

Step 4:

The test statistic is,

$\text{Test statistic, X}=min(X^+,X^-)=min(4,10)=4$

The critical value for the test statistic is obtained from the table of critical values for the sign test for significance level = 0.10 and n = 14,

$X_{cric}=3$

Step 5:

Since the test statistic, X = > Xcric = 3, the null hypothesis is not rejected hence we can not conclude that the median is different from 35.