Which statistical test is used to compare a sample mean to a known value when the population standard deviation is unknown?

• A. z-test
• B. ANOVA
• C. t-test (one-sample)
• D. chi-square test

Answer: (C)

When you’re comparing a sample mean to a known value and you don’t know the population standard deviation, you use a one-sample t-test. The t-test accounts for the extra uncertainty from estimating the spread with the sample standard deviation. You compute the t statistic as (sample mean − known value) divided by (sample standard deviation divided by the square root of the sample size). This statistic follows a t distribution with n−1 degrees of freedom, so you can assess significance using the t distribution or a p-value. If the population standard deviation were known, you’d use a z-test instead. ANOVA is for comparing means across three or more groups, and chi-square is for categorical data, not a single mean comparison.