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QuestionStatistics
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.
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Step 1: Define the sampling plan
To obtain a simple random sample of 1,000 customers from the list of 30,000, we can use a process called "random sampling without replacement." This means that every member of the population (the list of customers) has an equal chance of being selected, and once a member is chosen, they are not returned to the pool for further selection.
Step 2: Assign a unique identifier to each customer
To simplify the sampling process, assign a unique identifier (e.g., a number from 1 to 30,000) to each customer on the list. This will make it easier to randomly select 1,000 customers.
Final Answer
Once you have 1,000 unique identifiers, extract the corresponding customer names and addresses from the list. These 1,000 customers now form your simple random sample. By following this sampling plan, you ensure that each customer has an equal chance of being selected for the sample, and the results can be generalized to the entire population of 30,000 customers. This sampling method helps minimize bias and increases the reliability of the survey.
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