Question: Why do firms change ownership? One possible reason for acquisitions is that the new owners expect to be able to manage the operations more efficiently than the current management. This theory leads to testable hypotheses. For example, it predicts that productivity should increase following a takeover and also that firms changing ownership should have lower productivity than firms in general. A study of this situation examined the productivity year by year for some firms that changed ownership and other firms that did not change owners.26 In particular, they reported

These numbers display a very clear pattern. Plants that changed owners tended to be less efficient than no changers. But the differences after the change were declining in magnitude. This signifies that the productivity of changers relative to that of no changers was both low and declining before the ownership change, and increasing (albeit still low) after the ownership change. With one exception, all of the productivity differences are highly statistically significant.

a. In the last line of the preceding quote, explain what is implied by "highly statistically significant."

b. Consider the comparison of average productivity of firms that changed ownership (at the time of the change) to average productivity of firms that did not change ownership. Identify all elements of this hypothesis testing situation, in particular: the hypotheses, the sample data, the type of test used, and the assumptions being made.

c. One result they reported was "at the time of ownership change, productivity level was 3.9% lower as compared to plants that did not change ownership. The t-statistic is 9.10." Perform a hypothesis test based on this information and state your conclusion. You may assume reasonably large samples.

d. Why have they gone to the trouble of doing statistical hypothesis tests? What have they gained over and above simply observing and describing the productivity differences in their data?