Question

Indicate whether we should trust the results of the study. Is the method of data collection biased? If it is, explain why. Take a random sample of one type of printer and test each printer to see how many pages of text each will print before the ink runs out. Use the average from the sample to estimate how many pages, on average, all printers of this type will last before the ink runs out.

Short answer

Based on the information provided, the method of data collection doesn't appear to be inherently biased as the sample is randomly selected. However, without further information about how representative the sample is, or details about the conditions in which printers were used, it's impossible to say definitively whether we should trust the results.

Step-by-step solution

Analyze the Sample Selection

Analyzing the way the sample has been selected is essential to evaluate any possible bias. Here, it seems like the sample is selected randomly. This minimizes the potential for selection bias, implying that every printer has an equal chance of being selected irrespective of any characteristic of the printer. Thus, this appears unbiased.

Evaluate the Estimator

The estimator (the average number of pages a printer can print before the ink runs out) is evaluated using the sample. Here, the sample mean is used as an estimator for the population mean. However, the result will only be as reliable as the sample is representative of the population. If the sample randomly chosen was of high-quality printers, the estimate will be biased towards high values, and vice versa. Without knowledge about the representativeness of the sample, it's difficult to assert if the method is biased.

Evaluate the Generalization

The study looks to estimate a property of all printers of this type based on a sample. This is valid only if the sample is representative of the entire population. Again, as the sample selection was random, this generalization isn't inherently biased.

Check Additional Information

It would be crucial to check if there is any additional information that might impact the reliability of the result. For instance, if all the printers were used in the same conditions (same temperature, humidity, etc.) and the sample size is large enough, the result should be trustworthy.