QQuestionBiology
QuestionBiology
5. 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. Describe a sampling plan that could be used to obtain a simple random sample of 1,000 customers from the list.
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. Forty customers from the sample reported a problem. Of the 40 customers who reported a problem, 13 customers, or $32.5 \%$, reported a problem specifically with the power door locks.
(b) Explain why 0.325 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.
(c) Based on the results of the sample, give a point estimate of the number of new cars sold that experienced a problem with the power door locks within the first 5,000 miles driven.
Attachments
6 months agoReport content
Answer
Full Solution Locked
Sign in to view the complete step-by-step solution and unlock all study resources.
Step 1
To obtain a simple random sample of 1,000 customers from the list of 30,000 customers, we can use a random number generator to assign a unique random number to each customer. Then, we select the first 1,000 customers with the smallest random numbers as our sample. This ensures that every customer has an equal chance of being selected, and the selection of one customer does not affect the probability of selecting any other customer.
Step 2
We should not use 0.325 to estimate the population proportion of new cars sold that experienced a problem with the power door locks within the first 5,000 miles driven because the sample is not representative of the entire population. The sample of 1,000 customers was asked if they experienced any mechanical problems, not specifically about power door locks. Therefore, the proportion of customers who reported a problem with power door locks in this sample is not directly applicable to the entire population of 30,000 new cars.
Final Answer
The point estimate of the number of new cars sold that experienced a problem with the power door locks within the first 5,000 miles driven is approximately 9,750.
Need Help with Homework?
Stuck on a difficult problem? We've got you covered:
- Post your question or upload an image
- Get instant step-by-step solutions
- Learn from our AI and community of students