Question

a company has two offices with 50 employees each. The employees in each office report on their daily commute time the results are shown in the table. Is there a significant difference between the commute times for the two populations? Use a 0.05 significance level.​

Answer 1

Step-by-step explanation:

We want to compare the means, so find the difference and the corresponding standard deviation:

μ = μ₁ − μ₂

μ = 25 − 23

μ = 2

σ = √(σ₁²/n₁ + σ₂²/n)

σ = √(3.1²/50 + 3.2²/50)

σ = 0.63

Using a 95% confidence level, z = 1.96.  So the interval is:

CI = 2 ± 1.96 × 0.63

CI = 2 ± 1.2

There is a 95% probability that the true difference in means is between 0.8 and 3.2.  Since 0 is not in this interval, we can conclude that there is a significant difference between the commute times for the two populations.