a simple random sample of size n is drawn from a normally distributed population, and the mean of the sample…

a simple random sample of size n is drawn from a normally distributed population, and the mean of the sample is $\bar{x}$, 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.\n| confidence level | 90% | 95% | 99% |\n| ---- | ---- | ---- | ---- |\n| $z^{*}$ - score | 1.645 | 1.96 | 2.58 |\n$\bar{x}pm\frac{0.90cdot s}{sqrt{n}}$\n$\bar{x}pm\frac{0.99cdot s}{sqrt{n}}$\n$\bar{x}pm\frac{1.645cdot s}{sqrt{n}}$\n$\bar{x}pm\frac{2.58cdot s}{sqrt{n}}$

a simple random sample of size n is drawn from a normally distributed population, and the mean of the sample is $\bar{x}$, 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.\n| confidence level | 90% | 95% | 99% |\n| ---- | ---- | ---- | ---- |\n| $z^{*}$ - score | 1.645 | 1.96 | 2.58 |\n$\bar{x}pm\frac{0.90cdot s}{sqrt{n}}$\n$\bar{x}pm\frac{0.99cdot s}{sqrt{n}}$\n$\bar{x}pm\frac{1.645cdot s}{sqrt{n}}$\n$\bar{x}pm\frac{2.58cdot s}{sqrt{n}}$

Answer

Explanation:

Step1: Recall confidence - interval formula

The formula for the confidence interval of the population mean when the population standard - deviation is unknown (but we use the sample standard - deviation $s$ as an estimate) for a normal distribution is $\bar{x}\pm z^\frac{s}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $z^$ is the critical value, $s$ is the sample standard - deviation, and $n$ is the sample size.

Step2: Identify the $z^*$ value for 99% confidence level

From the given table, the $z^*$ value for a 99% confidence level is 2.58.

Step3: Write the 99% confidence interval

Substituting the $z^*$ value into the formula, we get $\bar{x}\pm\frac{2.58\cdot s}{\sqrt{n}}$.

Answer:

$\bar{x}\pm\frac{2.58\cdot s}{\sqrt{n}}$