Question

I want Example for Sign test for small sample

Answer 1

PROBLEM

We have sample scores (out of 15) of a quiz for 20 students of a class as follows.

9.3	8.8	10.7	11.5	8.2	9.7	10.3	8.6	11.3	10.7
11.2	9.0	9.8	9.3	9.9	10.3	10.0	10.1	9.6	10.4

Test whether population median score of all students of the course is 9.9 using one sample sign test at level of significance .

SOLUTION

We have to test for null hypothesis

against the alternative hypothesis

We put - sign if sample value is lesser than 9.9, + sign if sample value is greater than 9.9 and ignore otherwise.

So the sequence og signs is as follows.

-, -, +, +, -, -, +, -, +, +, +, -, -, -, +, +, +, -, +

Number of + sign

Number of - sign

So,

We define Bernoulli variate

Under Binomial distribution,

we have to test for null hypothesis

against the alternative hypothesis

Under ,

In case of two tailed test (not equal type alternative hypothesis) we reject our null hypothesis if .

Here we observe that .

So, we cannot reject our null hypothesis.

Hence, based on the given data we can conclude that there is not significant evidence that the population median quiz score differs from 9.9.