Question

What is the rationale and the steps behind calculating a confidence interval for the mean of a normal population when n is small using the formula: (1/x) ± (t critical value) (5/√n)?

Answer 1

To calculate a confidence interval for the mean of a normal population when n is small, use the formula (1/x) ± (t critical value) (5/√n) and follow these steps: calculate the point estimate, find the critical value, calculate the error bound, and construct the confidence interval.

Step-by-step explanation:

To calculate a confidence interval for the mean of a normal population when n is small, we can use the formula (1/x) ± (t critical value) (5/√n). Here are the steps:

1. Calculate the point estimate for the population mean.
2. Find the appropriate critical value from the t-distribution table based on the desired confidence level and degrees of freedom.
3. Calculate the error bound by multiplying the critical value with (5/√n).
4. Construct the confidence interval by subtracting the error bound from the point estimate to get the lower bound, and adding the error bound to the point estimate to get the upper bound.