Question

The ___________ is a minimum-variance unbiased point estimate of the mean of a normally distributed population

Answer 1

Answer:

Sample mean is the answer

Step-by-step explanation:

Recall the central limit theorem.

Suppose that a sample is obtained containing a large number of observations, each observation being randomly generated in a way that does not depend on the values of the other observations, and that the arithmetic mean of the observed values is computed. If this procedure is performed many times, the central limit theorem says that the distribution of the average will be closely approximated by a normal distribution. A simple example of this is that if one flips a coin many times the probability of getting a given number of heads in a series of flips will approach a normal curve, with mean equal to half the total number of flips in each series. (In the limit of an infinite number of flips, it will equal a normal curve.)

Hence we find that sample means is a minimum-variance unbiased point estimate of the mean of a normally distributed population

Answer 2

The Sample mean is a minimum-variance unbiased point estimate of the mean of a normally distributed population

Further Explanation:

Sample mean is the mean of sample data.

The sample parameter is an unbiased point estimated of the mean of a normally distributed population.

The sample parameter is sample mean.

An estimator is said to be an unbiased estimator if,

$\boxed{\theta = E\left( \theta \right)}$

An unbiased estimator is when the mean of the statistic’s sampling distribution is equal to the population’s parameter. This means the same estimate. If the statistic equals the parameter, then it’s unbiased estimator.

The biased estimator is the parameter when the sample parameter is not equal to the population parameter. This mean the sample mean is not equal to population mean.

Therefore, the Sample mean is a minimum-variance unbiased point estimate of the mean of a normally distributed population.

Learn more:

1. Learn more about normal distribution brainly.com/question/12698949

2. Learn more about standard normal distribution brainly.com/question/13006989

3. Learn more about confidence interval of mean brainly.com/question/12986589

Answer details:

Grade: College

Subject: Statistics

Chapter: Normal distribution

Keywords: standard normal distribution, standard deviation, test, measure, probability, low score, mean, repeating, indicated, normal distribution, percentile, percentage, undesirable behavior, proportion, unbiased estimator, unbiased, biased, minimum variance, normally distributed population.