CFA Level 1: Confidence Interval for Population Mean

Confidence Interval for Population Mean

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Question

A sample of size 225 is drawn from a population. The sample mean equals 876 and the variance of the sample equals 5,924. The 85% confidence interval for the population mean is given by:

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Explanation

If z is the z-value corresponding to the specified confidence level, the sample mean is M and the standard deviation is D in a sample size N, the confidence interval is specified as [M - z*D/sqrt(N), M + z*D/sqrt(N)]. In the present case, for the 85% confidence interval, the normal probability table gives z = 1.44. The sample standard deviation equals sqrt(5924) = 76.97. Therefore, the confidence interval equals [876 - 1.44*76.97/sqrt(225), 876 + 1.44*76.97/sqrt(225)] = [868.6,

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