a. Exercise 1—Sign Test

Are stock splits beneficial to stockholders? SNL Securities studied stock splits in the banking industry over an 18-month period and found that stock splits tended to increase the value of an individual’s stock holding. Assume that of a sample of 20 recent stock splits, 14 led to an increase in value, four led to a decrease in value, and two resulted in no change. Suppose a sign test is to be used to determine whether stock splits continue to be beneficial for holders of bank stocks.

1) What are the null and alternative hypotheses?

2) With α = .05, what is the rejection rule?

3) What is your conclusion?

(Reference: Anderson, Sweeney, Williams, 2002, print version, section 5, p. 381, exercise 3)

Solution to Exercise a.

1) We are interested on testing the following null hypothesis

against the alternative hypothesis

2) We need to apply the sign test with the significance level . We have to compute the following Z statistics

where:

K = # of times where the stock split led to an increase in value = 14

n = sample size = 20.

Therefore, we have that. For the significance level of, the rejection level is

We would reject the null hypothesis if Z>R. Since 1.788854>1.644853, there is enough evidence to reject the null hypothesis at the 0.05 level of significance. Therefore, we conclude that the splits are beneficial.

3) Our conclusion, based on the execution of the Sign Test, is that the stock splits continue to be beneficial for stock holders.