the true value of the population parameter is marked on each histogram,compare the bias of these estimates,and based on the performance of the three statistics in many samples,which is preferred as an estimate of the parameter?justify your answer.
To compare the bias of the estimates and determine which statistic is preferred as an estimate of the parameter, you can follow these steps:
Step 1: Understand Bias in Statistics
Bias measures how far off, on average, an estimate is from the true population parameter. A statistic is considered unbiased when the expected value of the statistic equals the true population parameter.
Step 2: Calculate Bias for Each Estimator
For each statistic, calculate the bias by finding the difference between the expected value of the statistic (E[statistic]) and the true population parameter (μ).
Step 3: Evaluate Bias in Many Samples
To assess bias in many samples, conduct a simulation study. Generate multiple random samples from the population and compute the estimates for each statistic. Calculate the average bias across all samples for each statistic.
Step 4: Compare Bias and Choose the Preferred Estimator
Compare the average bias for each statistic calculated in Step 3. The statistic with the smallest average bias is preferred as an estimate of the parameter.
Justification for Choosing the Preferred Estimator:
The preferred estimator should have the smallest bias on average. A smaller bias indicates that the estimator is more likely to be close to the true population parameter. The estimator with the smallest average bias is preferred as it provides more accurate estimates of the parameter.
Note: It's important to consider other properties, such as consistency and efficiency, alongside bias when choosing an estimator. However, since the provided question specifically asks about bias, this answer focuses on that aspect.