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A certain statistic d hat is being used to estimate a population parameter D. The expected value of d hat is not equal to D. What property does d hat exhibit?


A. The sampling distribution of d hat is normal.

B. The sampling distribution of d hat is binomial.

C. The sampling distribution of d hat is uniform.

D. d hat is unbiased.

E. d hat is biased.

Respuesta :

Answer:

the correct option is E. d is biased.

Step-by-step explanation:

As given,

The expected value of d hat is not equal to D.

We know that,

The unbiased-ness is the property that tells the expected value of d is equal to D

So, the correct option is E. d is biased.

Using the Central Limit Theorem for proportions, the correct option is:

E. The statistic is biased.

The Central Limit Theorem establishes that for a proportion p in a sample of size n:

  • The expected value is [tex]\mu = p[/tex].
  • The standard error is [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex]

In this problem, the expected value is different of the expected of [tex]\mu = p[/tex], hence, the statistic is biased, and the correct option is E.

For more on the Central Limit Theorem, you can check https://brainly.com/question/4086221

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