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Constructing Certain Types of Mean Intervals: Respect Your Boss

APSTAT-44FX4U

An insurance company is assessing two of its regional managers (Manager $A$ and Manager $B$) on how well-respected they are by their employees. The insurance company randomly selects $40$ employees from both regions.

They ask the employees to rate how much they respect their managers on a $1-10$ scale, with $1$ representing no respect and $10$ representing the utmost respect. Here are the summary results:

Company N Average Standard Deviation
A 40 8.1 1.4
B 40 6.2 1.1



Which of the following represents a $99\%$ confidence interval for the difference in the averages between how much company $A$'s employees respect their manager when compared with company $B$'s?

A

$(1.156,2.644)$

B

$(1.175,2.625)$

C

$(1.780,2.021)$

D

$(1.785,2.015)$

E

$(6.200,8.100)$