Explain how the confidence interval of the mean is affected by (all other factors constant). a) Number of samples N b) Confidence level c) Standard deviation

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Explain how the confidence interval of the mean is affected by (all other factors constant).
a) Number of samples N
b) Confidence level
c) Standard deviation

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The confidence interval is the interval in which the population parameter is likely to fall. Let xi; (i=1,2,...,N) be the random sample of size N from the normal population with mean μ and variance σ2. The sample mean x¯ is normally distributed with mean μ and variance σ2/N. For large samples, the confidence interval at the α% level of significance for population mean μ is given as follows:

x¯±Zα%×σN

When population variance is unknown, we will use its estimate, i.e., sample variance, s2.

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