Question

The authors of a certain paper describe a study to evaluate the effect of mobile phone use by taxi drivers in Greece. Fifty taxi drivers drove in a driving simulator where they were following a lead car. The drivers were asked to carry on a conversation on a mobile phone while driving, and the following distance (the distance between the taxi and the lead car) was recorded. The sample mean following distance was 3.70 meters and the sample standard deviation was 1.17 meters.
a. Construct and interpret a 95% confidence interval for m, the population mean following distance while talking on a mobile phone for the population of taxi drivers.
b. What assumption must be made to generalize this confidence interval to the population of all taxi drivers in Greece?

Answer 1

Answer:

The answer is below

Step-by-step explanation:

The mean (μ) = 3.7 m, standard deviation (σ) = 1.17 m, confidence (C) = 95% = 0.95, sample size (n) = 50

a) α = 1 - C = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

The z score of α/2 is the same as the z score of 0.475 (0.5 - 0.025) which is 1.96. Hence:

The margin of error (E) = $z_\frac{\alpha}{2} *\frac{\sigma}{\sqrt{n} }=1.96*\frac{1.17}{\sqrt{50} } =0.32$

The confidence interval = μ ± E = 3.7 ± 0.32 = (3.38, 4.02)

b) This means that we are 95% sure that any distance between the taxi and the lead car is between 3.38 m and 4.02 m