A random sample of size 50 has been taken from normal population. The mean of th

Question

A random sample of size 50 has been taken from normal population. The mean of this sample was calculated to be 104 with a 95% confidence interval of (94.3, 113.7). Discuss whether the following possible interpretations for this interval are valid or not, and why.

(a) About 95% population means µ lie between 94.3 and 113.7.

(b) There is only 5% of the population means µ lie outside (94.3, 113.7).

(c) I am 95% confident in this interval because the procedure I used is correct 95% of the time.

(d) If one were to repeat this experiment taking a sample of size of 25, and got the same sample mean, then we are 95% confidence that µ will fall in the interval (94.3, 13.7)

(e) If one were to repeat this experiment many times, taking samples of size 25 and calculating a confidence interval from each sample, then approximately 95% of the intervals found will contain µ.

(f) If one were to repeat this experiment many times, taking samples of size 25 and calculating a sample mean from each sample, then about 95% of the means will be in the interval (94.3,113.7).

Explanation / Answer

the correct answer is

(b) There is only 5% of the population means µ lie outside (94.3, 113.7).

and

(a) About 95% population means µ lie between 94.3 and 113.7.

the other answers are confused and dont have nothing with a confidence interval

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