A random sample has been taken from a normal distribution and the following confidence intervals constructed using the same data
: (25.53, 37.87) and (23.59, 39.81). One of these intervals is a 99% CI and the other is a 95% CI. Please match them.
1 answer:
Answer:
(25.53, 37.87): 95% CI
(23.59, 39.81): 99% CI
Step-by-step explanation:
The margin of error of a confidence interval is given by:

In which
is the standard deviation of the population and n is the size of the sample.
z is related to the confidence level. The higher the confidence level, the higher the values of z, and thus, we wider the confidence interval is.
In this question:
The narrower C.I. is the 95%, and the wider is the 99%. So
(25.53, 37.87): 95% CI
(23.59, 39.81): 99% CI
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