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

Solution:-

(A)

Both Z score and t statistic have equal numerator, but they are different in terms of standard error calculation (denominator). T statistic are more variable than Z score. This is caused by extra variability of sample variance in t static with respect to Z. Epecially in small sample size its power is greater than for same significance level. So generally we can say that t test is more robust

B)

Due to critical t value which is higher than Z value.

t confidence inerval

t Z - confidence interval

(C)

student t distribution is a continuous probability distribution which is appled as below.

where

Z N(0, 1)

is a chi square random variable with D degree of freedom.

pdf:

He invented because he felt big sample to select best yielding varieties of barely (which he was worked) was telious. So he developed a way to extract a small samples, result in new discovery of t distribution.