Assume that matched pairs of data result in the given number of signs when the value of the second variable is subtracted from the corresponding value of the first variable. Use the sign test with a 0.05 significance level to test the null hypothesis of no difference.
Positive signs: 13; negative signs: 1; ties: 0 (from a preliminary test of the MicroSort method of gender selection)
The null hypothesis is the claim of no difference between the gender selections.
H0: There is no difference between the gender selections.
H1: There is a difference between the gender selections.
Its given that the number of positive signs = 13
Number of negative signs = 1
Number of ties = 0
So the Sample size that is used for the sign test n = 14
As the sample size n = 14 is less than 25 that is .
Therefore the value of the test statics is the number of times the less frequent sign occurs which in present case is the negative sign.
Thus value of the test statics x = 1.
As the test is a two tailed test, with n = 14 and a = 0.05 significance level , the critical value is 2.
But x = 1, which is less than 2. So the critical value is greater than the number of times less frequent sign occurs.
Hence, the Null hypothesis is rejected. And the alternative hypothesis is accepted
That is there is a difference.
Interpretation : Therefore, it can be said that there is a difference in the gender selection.