In what ways are companies that fail different from those that continue to do business? To answer this question, one study compared various characteristics of74

74active and27

27failed retail firms. One of the variables was the cash flow margin. Roughly speaking, this is a measure of how efficiently a company converts its sales dollars to cash and is a key profitability measure. The higher the percent, the more profitable thecompany.

Using the pooled twosample procedure, the difference between the cash flow margins for active and failed companies was statistically significant(=2.85,df=99,=0.005).

(t=2.85,df=99,P=0.005).Because this study is a couple of years old, the researchers plan a similar study to determine if these findings continue tohold.

Should a new sample have similar numbers of firms? Is it possible to save resources by using smaller samples and still be able to declare that the successful and failed firms are different? To answer this question, the researchers did some power calculations where they used the alternative

1

2

=12.00,

12=12.00,chose the level of significance=0.05,

=0.05,and took the pooled value from the previous study,=19.59.

s=19.59.

If the true population standard deviation were25

25instead of the19.59

19.59hypothesized, would the power increase ordecrease?

Decrease. A larger standard deviation makes it more difficult to detect the givendifference.

Decrease. A larger standard deviation increases the number of degrees of freedom, which makes the test lesspowerful.

Increase. A larger standard deviation decreases the probability of a type II error, which increasespower.

Increase. A larger standard deviation makes it easier to detect the givendifference.