Do Dallas plant personnel take more sick days than Philadelp

Do Dallas plant personnel take more sick days than Philadelphia plant personnel? The sample mean for Dallas is 4.5 days, and the sample mean for Philadelphia is 4.1days. A 95 percent confident interval is (4.5 - 4.1) ± .2. What can we conclude (Multiple choice) and why (need the reasons as to why and why not)?

a. We cannot detect a difference in sick days taken between the two plants.

b. It is too close to tell. We have to take larger size samples.

c. We can detect a difference; Dallas plant workers take more sick days.

d. We can detect a difference; Philadelphia plant workers take more sick days.

Thank you!

Solution

a. We cannot detect a difference in sick days taken between the two plants.

as you can see we cannot detect a difference in sick days taken between the 2 plants

4.5 - 4.1 = 0.4 +/- 0.2

if we can detect a difference , the difference will be significance but for this confidence interval is not significant