Question

If sigma is known, n < 30, and you have no information about the population distribution. Which would be the correct course of action to take to find the confidence interval? (a) Use the t-formula (b) Use the z-formula (c) Something else

Answer 1

If sigma is known, n < 30, t- formula would be the correct course of action to take to find the confidence interval.

With smaller samples (n< 30) the Central Limit Theorem does not apply, and the distribution called the t distribution must be used. The t distribution is similar to the standard normal distribution but takes a slightly different shape depending on the sample size. In a sense, one could think of the t distribution as a family of distributions for smaller samples. Instead of "Z" values, there are "t" values for confidence intervals which are larger for smaller samples, producing larger margins of error, because small samples are less precise. t values are listed by degrees of freedom (df). Just as with large samples, the t distribution assumes that the outcome of interest is approximately normally distributed.