A random sample has been taken from a normal population and

A random sample has been taken from a normal popula­tion and two confidence intervals constructed using exactly the same data. The two CI s are (38.02, 61.98) and (39.95, 60.05).

(a)        What is the value of the sample mean?

(b)        One of these intervals is a 90% CI and the other is a 95% CI. Which one is the 95% CI and why

Solution

a)

Sample mean = (upper bound + lower bound)/2

Using any of the intervals (but we choose the first one,

sample mean = (38.02 + 61.98)/2 = 50 [ANSWER]

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b)

Higher confidence levels yield wider confidence intervals.

Thus, the 95% confidence interval is (38.02, 61.98) and the 90% confidence is (39.95, 60.05). [ANSWER]