Question

a simple random sample of size n is drawn from a normally distributed population, and the mean of the sample is x, while the standard deviation is s. what is the 99% confidence interval for the population mean? use the table below to help you answer the question. confidence level 90% 95% 99% z*-score 1.645 1.96 2.58 x±0.90·s/√n x±0.99·s/√n x±1.645·s/√n x±2.58·s/√n

Explanation:

Step1: Recall the confidence interval formula

The formula for the confidence interval for the population mean when the population standard deviation is unknown (using sample standard deviation \(s\)) is \(\bar{x}\pm z^{*}\frac{s}{\sqrt{n}}\), where \(z^{*}\) is the critical value.

Step2: Identify the \(z^{*}\) - value for 99% confidence level

From the given table, for a 99% confidence level, the \(z^{*}\) - score is \(2.58\).

Answer:

\(\bar{x}\pm\frac{2.58\cdot s}{\sqrt{n}}\) (the fourth option)