Question

5 A) Inferences based on t-statistics are said to be more robust than those using z-statistics. Explain what this means.

B) Confidence intervals using t-statistics are generally broader than those using z-statistics. Explain why this is.

C) Explain as completely as possible what a Student’s t distribution is and why William Gosset developed it.

Answer 1

Both Z score and T statistic have equal numerator but they're different in terms of ordinary error calculation (denominator) T statistic are more variable then Z score: this is often caused by extra variability of sample variance in statistic with reference to Z. Especially in small sample size its power is bigger then for same significance level so generally we will say that T test is more robust