cimmerian said:I'm supposed to find the 100(1 - alpha) confidence interval for μ
A confidence interval is a range of values that are likely to contain the true population parameter with a certain level of confidence. In this case, it refers to the range of values for the population mean, μ, with a specified level of confidence.
When μ and σ^2 are unknown, we cannot make accurate statements about the population mean based on a single sample. Using a confidence interval allows us to estimate the range of values for μ with a certain level of confidence, making our conclusions more reliable.
The confidence level is typically chosen by the researcher and represents the probability that the confidence interval will contain the true population parameter. It is often set at 95% or 99%.
The formula is: x̄ ± tα/2 * s/√n, where x̄ is the sample mean, tα/2 is the t-critical value based on the desired confidence level and sample size, s is the sample standard deviation, and n is the sample size.
Increasing the sample size decreases the width of the confidence interval. This is because a larger sample size leads to a more precise estimate of the population mean, resulting in a narrower range of values for the confidence interval.