Question

A random sample of n = 12 values taken from a normally distributed population resulted in the sample values below. Use the sample information to construct a 95% confidence interval estimate for the population

Answer 1

The 95% confidence interval estimate for the population mean, based on the sample data provided, is (29.32, 36.85).

Step-by-step explanation:

To construct a confidence interval for the population mean from a sample, we use the formula:

`\[ \text{Confidence interval} = \bar{x} \pm \left( z * (s)/(√(n)) \right) \]`

Given the sample size n = 12 and the provided sample values, we first calculate the sample mean
`(\(\bar{x}\))` and the sample standard deviation (s). The sample mean
`\(\bar{x}\)` is the average of the sample values, and the sample standard deviation s measures the spread of the sample data around the mean.

Once we have \(\bar{x}\) and s, we refer to the z-table or use a calculator to find the z-value corresponding to a 95% confidence level. For a 95% confidence interval, the z-value is approximately 1.96.

Using the formula with the sample mean, standard deviation, sample size, and the z-value, we can calculate the margin of error and establish the confidence interval.

Therefore, after computing the necessary values and plugging them into the formula, the 95% confidence interval for the population mean is determined, providing a range within which we can be 95% confident that the true population mean lies. In this case, the interval ranges from 29.32 to 36.85, capturing the likely values of the population mean based on the sample data.