When finding a confidence interval for a population mean based on a sample of size 11, which assumption is made?


The standard deviation is fixed.

The sampling distribution of z is normal.

The sampling distribution of the sample means is approximately normal.

There is no special assumption made.

When finding a confidence interval for a population mean based on a sample of size 11, the assumption made is that the sampling distribution of the sample means is approximately normal.

To understand why this assumption is made, let's break it down:

A confidence interval is a range of values estimated from a sample data that is likely to contain the true population parameter, in this case, the population mean.

The central limit theorem states that for large enough sample sizes (typically 30 or more), the sampling distribution of the sample means is approximately normally distributed, regardless of the distribution of the population.

However, for smaller sample sizes, like 11 in this case, the assumption is made that the sampling distribution of the sample means is still approximately normal. This assumption holds if the population distribution is symmetric or not heavily skewed.

By assuming the approximate normality of the sampling distribution, various statistical techniques can be used to estimate the population mean and construct the confidence interval.

So, the correct answer is: The sampling distribution of the sample means is approximately normal.