A new manager,hired at a large warehouse,was told to reduce the employee sick leave.The manager introduced a new incentive program for employees with perfect attendance.Suppose the proportion of the employees sick prior to the new program is
And the employees sick after the new program is
.A study found a 98% confidence interval for
-
Is (-0.0668,0.1125).Give an interpretation of this confidence interval.
A)We know that 98% of the employees sick after the new program is between 6.68% less and 11.25% more than the employees sick prior to the new program.
B)We are 98% confident that the proportion of the employees sick prior to the new program is between 6.68% less and 11.25% more than the proportion of the employees sick after the new program.
C)We know that 98% of all random samples done on the population will show that the proportion of the employees sick prior to the new program is between 6.68% less and 11.25% more than the proportion of the employees sick after the new program.
D)We know that 98% of the employees sick prior to the new program is between 6.68% less and 11.25% more than the employees sick after the new program.
E)We are 98% confident that the proportion of the employees sick after the new program is between 6.68% less and 11.25% more than the proportion of the employees sick prior to the new program.

Question

A new manager,hired at a large warehouse,was told to reduce the employee sick leave.The manager introduced a new incentive program for employees with perfect attendance.Suppose the proportion of the employees sick prior to the new program is 
And the employees sick after the new program is 
.A study found a 98% confidence interval for 
- 
Is (-0.0668,0.1125).Give an interpretation of this confidence interval.
A)We know that 98% of the employees sick after the new program is between 6.68% less and 11.25% more than the employees sick prior to the new program. 
B)We are 98% confident that the proportion of the employees sick prior to the new program is between 6.68% less and 11.25% more than the proportion of the employees sick after the new program. 
C)We know that 98% of all random samples done on the population will show that the proportion of the employees sick prior to the new program is between 6.68% less and 11.25% more than the proportion of the employees sick after the new program. 
D)We know that 98% of the employees sick prior to the new program is between 6.68% less and 11.25% more than the employees sick after the new program. 
E)We are 98% confident that the proportion of the employees sick after the new program is between 6.68% less and 11.25% more than the proportion of the employees sick prior to the new program.

Quizplus · Accepted Answer

The confidence interval (-0.0668, 0.1125) represents a range of plausible values for the difference between the proportion of employees sick prior to the new program and the proportion of employees sick after the new program. We can interpret this interval as saying that we are 98% confident that the true difference in proportions is somewhere between a reduction of 6.68% and an increase of 11.25%, compared to the proportion before the new program was implemented. Therefore, choice B is the best choice as it accurately reflects this interpretation.

A New Manager,hired at a Large Warehouse,was Told to Reduce