In creating a confidence interval for the population mean, if σ is unknown, we estimate it using which of the following?
When the population standard deviation (σ) is unknown, we estimate it using the sample standard deviation (s)
When the population standard deviation (σ) is unknown, we estimate it using the sample standard deviation (s). Essentially, we use the data from a sample to estimate the variability in the population.
To create a confidence interval for the population mean, we typically use the t-distribution when the sample size is small (less than 30) or when the population distribution is unknown or not approximately normal. The formula for the confidence interval is as follows:
Confidence Interval = X̄ ± (t * (s/√n))
Here, X̄ represents the sample mean, t represents the critical value from the t-distribution based on the desired confidence level, s is the sample standard deviation, and n is the sample size.
By substituting the sample mean, sample standard deviation, and the appropriate critical value from the t-distribution into the formula, we can estimate the range within which the population mean is likely to fall with a certain degree of confidence.
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