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 $p _ { p }$ and the employees sick after the new program is $Pa\mathrm { Pa }$ .A study found a 98% confidence interval for $p _ { p }$ - $Pa\mathrm { Pa }$ 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

p _ { p }

and the employees sick after the new program is

Pa\mathrm { Pa }

.A study found a 98% confidence interval for

p _ { p }

-

Pa\mathrm { Pa }

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.

danielle wickman · Accepted Answer

Final Answer : B, Explanation :  The correct interpretation of a confidence interval is about our confidence in the interval itself capturing the true difference between two parameters (in this case, the proportion of employees sick before and after the program), not about the proportion of samples or individuals within that interval. Choice B correctly states that we are 98% confident that the true difference in proportions falls within the given range, with the proportion of employees sick before the program being potentially less or more than the proportion after the program by the specified percentages.

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