Clarification of confidence interval

[watashi]

Just a single tricky question, for learning purpose, I'd appreciate who can tell me what to change to make it correct:

Which of the followings is true?

a) If a research draws 10000 random samples, each of a sample size 1000, he expects about 500 of his sample would not include the population mean
b) Confidence intervals can be derived for both population means and population proportions
c) Confidence intervals can be derived for both sample means and sample proportions

[zmogggggg]

a) your sample mean and sample variance (estimators) attain population mean and population variance on average; this says nothing about your individual sample values. I'd say false.
b) true, one method of derivation is via the Pivot Method
c) false, confidence intervals are constructed for unknown parameter values, not estimates

[watashi]

Why is this false?
a) If a research draws 10000 random samples, each of a sample size 1000, he expects about 500 of his sample would not include the population mean

a) your sample mean and sample variance (estimators) attain population mean and population variance on average; this says nothing about your individual sample values. I'd say false.

I don't quite understand what your explanation refers to. Would you mind refering to the figures? Thanks again

[vinux]

Just a single tricky question, for learning purpose, I'd appreciate who can tell me what to change to make it correct:

Which of the followings is true?

a) If a research draws 10000 random samples, each of a sample size 1000, he expects about 500 of his sample would not include the population mean

I don't think it is false. In a continuous population, Probability of getting a particular number is close to zero( meaningless).

I will give an extreme example. Suppose a population contains only 0 & 1 . Assume that population mean =0.5 (50:50)

0.5 will not be present in any of the sample.