Question

Studies show that drivers who use cell phones while driving increase their risk of an accident. In a sample of 371 cases of new drivers using a cell phone while driving, 24 resulted in a crash. Find a 99% confidence interval estimate of the true population proportion of new drivers who were in a crash while using their cell phone.

Answer 1

The 99% confidence interval estimate of the true population proportion of new drivers who were in a crash while using their cell phone is 0.0647 +/- 0.0330 = (0.0317, 0.0977)

Explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

p+/-z√(p(1-p)/n)

Given that;

Proportion p = 24/371 = 0.0647

Number of samples n = 371

Confidence interval = 99%

z(at 99% confidence) = 2.58

Substituting the values we have;

0.0647 +/- 2.58√(0.0647(1-0.0647)/371)

0.0647 +/- 0.032950374780

0.0647 +/- 0.0330

(0.0317, 0.0977)

The 99% confidence interval estimate of the true population proportion of new drivers who were in a crash while using their cell phone is 0.0647 +/- 0.0330 = (0.0317, 0.0977)