Question

Construct a confidence interval for μ assuming that each sample is from a normal population. Please show how to do this in excel (a)x⎯⎯x¯ = 23, σ = 3, n = 12, 90 percentage confidence. (Round

Answer 1

The 90% confidence interval for the population mean (μ) is approximately [21.40, 24.60].

Step-by-step explanation:

To construct a confidence interval for μ, we use the formula:
`\(\bar{x} \pm Z * (\sigma)/(√(n))\), where \(\bar{x}\)` is the sample mean, σ is the population standard deviation, n is the sample size, and Z is the Z-score corresponding to the desired confidence level.

For the given data
`(\(\bar{x} = 23, \sigma = 3, n = 12\)`, and 90% confidence), we find the Z-score for a 90% confidence interval, which is approximately 1.645.

Substituting the values into the formula, we get
`\(23 \pm 1.645 * (3)/(√(12))\).` Calculating this gives us the interval [21.40, 24.60].

This means we are 90% confident that the true population mean falls within this interval. The wider the interval, the greater the level of confidence we can have in capturing the true population mean. In this case, the interval [21.40, 24.60] suggests that, based on the sample data, we are quite confident that the true population mean is within this range.