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?

a. The population of taxi drivers in Greece falls between 3.3766 meters and 4.0234 meters.

b. The assumption is that the sample of 50 taxi drivers is representative of the population.

a.

To construct a 95% confidence interval for the population mean following distance while talking on a mobile phone, we can use the formula:

Confidence Interval = sample mean ± (critical value × standard error)

The standard error:

Standard Error = sample standard deviation / √(sample size)

Standard Error = 1.17 / √(50)

Standard Error = 0.165

Since the sample size is large (n > 30), we can use the Z-table to find the critical value.

For a 95% confidence level, the critical value is approximately 1.96.

Now we can construct the confidence interval:

Confidence Interval = 3.70 ± (1.96 × 0.165)

Confidence Interval = 3.70 ± 0.3234

Confidence Interval = (3.3766, 4.0234)

Interpretation: We are 95% confident that the true population means following distance while talking on a mobile phone for the population of taxi drivers in Greece falls between 3.3766 meters and 4.0234 meters.

b.

The assumption that must be made to generalize this confidence interval to the population of all taxi drivers in Greece is that the sample of 50 taxi drivers is representative of the population. It is assumed that the sample was randomly selected and that the taxi drivers included in the study are a fair and unbiased representation of all taxi drivers in Greece.

Learn more about the confidence interval here:

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