Answer to Question #169205 in Statistics and Probability for DINESH KUMAR SONI

Question

Use the sign test to see if there is a difference between the number of days required to collect an account receivable before and after a new collection policy. Use the 0.05 significance level. 

Before 33 36 41 32 39 47 34 29 32 34 40 42 33 36 27 After 35 29 38 34 37 47 36 32 30 34 41 38 37 35 28 

Answer 1

$H_0 : μ_{before} = μ_{after} \\ H_1 : μ_{before} ≠ μ_{after}$

The number of plus and minus signs for each pair is shown along with the raw data in the table above. From the above we see that there are 7 (−)ve signs, 6 (+)ve sings and 1 zero. As per the convention we drop the pair giving rise to zero. Then n = 15 − 1 = 14 and S = 6 as the (+)ve sing is less frequent. Calculating the value of K we have:

$K = \frac{14-1}{2} - 0.98 \sqrt{14} = 6.50 -3.67 = 2.83$

Since S > K the null hypothesis is accepted and we may conclude that there is no significant difference between the number of days required to collect an account receivable before and after a new collection policy.