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.

Question

Brindle

Mathematics

21 February, 02:31

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.

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Nia · 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)

Step-by-step 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)