Consider a 95% confidence interval for the mean height µ in a population. Which

Question

Consider a 95% confidence interval for the mean height µ in a population. Which of the following are true or false: (Please provide your explanations)

(a) Before taking our sample, the probability of the resulting 95% confidence interval containing µ is 0.95.

(b) Out of one hundred 95% confidence intervals for µ, on average 5 will contain µ.

(c) 95% of individuals in the population have heights that lie in the 95% confidence interval for µ.

(d) Before taking our sample, the center of a 95% confidence interval for the population mean is a random variable.

Explanation / Answer

ANS (A)  Before taking our sample, the probability of the resulting 95% confidence interval containing µ is 0.95.

is true and rest are falls

Explanation:if we take sample repeatedly from normal population and for each sample we compute this random interval [T1,T2] then relative frequency of those interval which contain true value of unknown parameter (meu) tend to (1-alpha) in the sense we say random interval [t1,t2] is .95 confidence interval for meu

(B) is totally wrong because it says Out of one hundred 95% confidence intervals for µ, on average 5 will contain µ

(D) statement in this is wrong because population paremeter is fixed quantity that lie in between two random points

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