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 3.80 meters and the sample standard deviation was 1.19 meters.

Construct a 95% confidence interval (in meters) for μ, the population mean following distance while talking on a mobile phone for the population of taxi drivers. (Round your answers to three decimal places.)

Answer 1

CI = (3.462, 4.138)

Explanation:

We are given;

Sample mean; x¯ = 3.8

Sample standard deviation; s = 1.19

Sample size; n = 50

DF = n - 1 = 50 - 1 = 49

Confidence level; CL = 95%

Significance level = (1 - 0.95)/2 = 0.025

Now,from the table attached using DF = 49, significance level = 0.025, one tail and by interpolation, we have; t = 2.01

Now, formula for confidence interval is;

CI = x¯ ± t(s/√n)

CI = 3.8 ± 2.01(1.19/√50)

CI = 3.8 ± 0.338

CI = (3.8 - 0.338, 3.8 + 0.338)

CI = (3.462, 4.138)