Define the sample mean and the population mean. 1.2 Define a point estimator of

Question

Define the sample mean and the population mean. 1.2 Define a point estimator of some population parameter theta. 1.3 In your own words (don't copy from the book or notes) what does the central limit theorem tell us? 1.4 What is an unbiased estimator of a parameter theta? 1.5 If a point estimator Z^^of Z is not unbiased, what is the bias? 1.6 Define the standard error of an estimator theta. 1.7 What is the sample mean if the N observations in a sample are x_1, x_2, ..., x_y? 1.8 For the N observations in 1.7 give the sample variance. 1.9 If a population has a mean w and a standard deviation a, what are the expected values of the unbiased estimators X^- and s of mu and sigma respectively?

Explanation / Answer

1.1

Sample mean is the average of the sample units taken from a population whereas population mean is the average of the entire population. Sample mean is denoted by "X" whereas population mean is denoted by letter “µ.”.

1.2

A point estimate of a population parameter is a single value of a statistic. That value represents the estimate for the entire population as a whole. For example, the sample mean x is a point estimate of the population mean ?. Similarly, the sample proportion p is a point estimate of the population proportion P.

1.3

The central limit theorem states that as the sample gets large enough, the sampling distribution of the sample mean becomes almost normal regardless of the shape of the population.

1.4

In statistics, the bias of an estimator arises when there is a difference between this estimator's expected value and the true value of the parameter being estimated. On the other way round, an estimator or decision rule with zero bias is called unbiased estimator of the population parameter.

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.