Question

The speed of pickup of ride sharing services like Uber and Lyft seems to have surpassed that of ambulance services. The mean response time of ambulances across the United States is 15.3 minutes with a standard deviation of 12.8 minutes. For ride sharing services, the mean pick-up time across the United States is 8 minutes with a standard deviation of 5.2 minutes. Based on these estimates, which of the following gives the standard deviation of the sampling distribution of the difference in the sample means for samples of 30 ambulance rides and 40 ride sharing rides (Ambulance – Ride Sharing)?

Answer 1

Explanation:

The correct answer is (C).

Because the sample sizes are less than 10% of their respective population sizes, the standard deviation of the difference in sample means is approximately \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}} = \sqrt{\frac{12.8^2}{30}+\frac{5.2^2}{40}} \approx 2.912

n

1

​

s

1

2

​

​ +

n

2

​

s

2

2

​

​

​ =

30

12.8

2

​ +

40

5.2

2

​

​ ≈2.912 minutes.

Answer 2

The correct answer is (C).

Because the sample sizes are less than 10% of their respective population sizes, the standard deviation of the difference in sample means is approximately≈2.912 minutes.

​

​

Explanation: