Respuesta :
Answer:
B. Sample mean used to estimate a population mean.
C. Sample variance used to estimate a population variance.
D. Sample proportion used to estimate a population proportion.
Step-by-step explanation:
This is because the mean of the sampling distribution of the mean tends to target the population mean. Also, the mean of the sampling distribution of the variance tends to target the population variance.
This means that the sample mean and variance tend to target the population mean and variance, respectively, instead of systematically tending to underestimate or overestimate that value. This is why sample means and variances are good estimators of population means and variances, respectively. This is also true for proportions but not true for medians, ranges and standard deviations.
This is about biased or unbiased estimation in distribution in statistics.
Options B, C & D are correct.
- Option A; This is not an unbiased estimator of population median because odd and even sample size tend to create different means of getting the median. Thus, it will be biased.
- Option B; The mean of the distribution of all sample means is also referred to as Expected Value of the sample mean. This expected value is always equal to the population mean. Thus, the sample mean is an unbiased estimator of the population mean.
- Option C; Sample mean is directly related to Sample variance. This means a higher value of Expected value of sample mean means a higher value of Expected value of of the sample variance. This means the expected value of the sample variance is also equal to the population variance. Thus, the sample variance is an unbiased estimator of the population variance.
- Option D; Sample proportion is akin to sample mean and as such follows the same reasoning for it being an unbiased estimator of the population proportion.
- Options E & F; The estimation does not apply in both cases.
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