The manager of the customer service division of a consumer electronics company was interested in determining whether customers who had purchased a DVD player over the past 12 months were satisfied with their products. Using the warranty cards submitted after purchases, the manager was planning to survey these customers. If the manager wanted to select a sample of warranty cards for each brand of DVD player sold, how should the sample be selected?Explain
The manager should use stratified sampling to select a sample of warranty cards for each brand of DVD player sold. Stratified sampling involves dividing the population into distinct groups, or strata, based on a specific characteristic - in this case, the brand of DVD player.
Here's a step-by-step process of selecting the sample using stratified sampling:
1. Identify the different brands of DVD players sold by the company in the past 12 months.
2. For each brand, create a separate list of warranty cards submitted by customers.
3. Determine the sample size for each brand. The manager can either select an equal sample size for each brand or use proportionate sampling, in which the sample size for each brand is proportional to the number of warranty cards submitted for that particular brand.
4. Use a random sampling method (such as simple random sampling) to select the desired number of warranty cards from each brand's list.
5. Combine the selected warranty cards from all brands to create the final sample.
By using stratified sampling, the manager ensures that each brand of DVD player is represented in the sample, which would provide more accurate insights into customer satisfaction across different brands.
To select a sample of warranty cards for each brand of DVD player sold, the manager can follow a systematic random sampling approach. This approach ensures that the sample represents the larger population accurately. Here's how it could be done:
1. Obtain a list of all DVD player brands sold by the company over the past 12 months.
2. Assign a unique identifier to each brand, such as a number or code.
3. Determine the desired sample size for each brand. This can be based on statistical calculations or managerial judgment.
4. Calculate the sampling interval, which is the total number of warranty cards divided by the desired sample size. For example, if there are 1,000 warranty cards and the desired sample size is 100, the sampling interval would be 10.
5. Start with a random number between 1 and the sampling interval.
6. Select the warranty card corresponding to that random number and record the brand.
7. Continue selecting every nth warranty card based on the sampling interval, where n is the brand's unique identifier.
8. Repeat steps 5-7 until the desired sample size for each brand is reached.
By following this systematic random sampling approach, the manager will obtain a representative sample that includes customers who purchased each brand of DVD player. This approach ensures that customers' opinions are accurately represented and can be used to assess satisfaction levels with the products.
To select a sample of warranty cards for each brand of DVD player sold, the manager can use a technique called stratified sampling. Here's how the sample selection process can be carried out:
1. Identify the different brands of DVD players sold by the company. This will be the basis for creating the strata.
2. Determine the proportion of customers who purchased each brand of DVD player. This can be done by looking at sales data or other relevant information.
3. Calculate the desired sample size for each brand. This can be determined based on the desired level of confidence and margin of error for the survey.
4. Multiply the proportion of customers who purchased each brand by the desired sample size to get the number of warranty cards to be selected for each brand. This will ensure that the sample is representative of the distribution of DVD player brands sold.
5. Randomly select the specified number of warranty cards from each brand. This can be done using a random number generator or any other suitable method.
By using stratified sampling, the manager ensures that each brand of DVD player is represented in the sample according to its proportion of sales. This helps in obtaining a more accurate and representative picture of customer satisfaction for each brand.