Question

An automobile manufacturer sold 30,000 new cars, one to each of 30,000 customers, in a certain year. The manufacturer was interested in investigating the proportion of the new cars that experienced a mechanical problem within the first 5,000 miles driven. a) A list of the names and addresses of all customers who bought the new cars is available. Each customer from a simple random sample of 1,000 customers who bought one of the new cars was asked whether they experienced any mechanical problems within the first 5,000 miles driven. 400 customers from the sample reported a problem. Of the 400 customers who reported a problem, 140 customers, or 32.5%, reported a problem specifically with the power door locks. Explain why 0.35 should not be used to estimate the population proportion of the 30,000 new cars sold that experienced a problem with the power door locks within the first 5,000 miles driven.

Answer 1

The reason that 0.35 should not be used to estimate the population proportion of the 30,000 new cars sold that experienced a problem with the power door locks within the first 5,000 miles driven is that 0.35 does not represent the sample proportion.

The correct sample proportion is 0.14 (140/1,000) and not 0.35 (140/400). It is this that can be used to estimate the population proportion and not 0.35.

Explanation:

a) Data and Calculations:

New cars sold by the automobile manufacturer = 30,000

Number of customers that the 30,000 new cars were sold to = 30,000

Simple random sample = 1,000 customers

Number of customers from the SRS that reported a problem = 400

This is equal to 40% of the sample (400/1,000 * 100)

Proportion of customers who reported a problem (specifically) with the power door locks = 140/400 = 0.35

Proportion of customers out of the sample that reported specifically a problem with the power door locks = 140/1000 = 0.14.