) Accurate to the nearest 3 decimal places, what is the critical value (tor z) that corresponds to the given confidence levels and degrees of freedom? Fill in the following table with the appropriate critical values from the t-table (table D). Remember to truncate down the df when the exact value is not listed in the table.

Confidence Level

Sigma unknown (t*)

df=23

df=55

df=97

Sigma known (z*)

70%
95%
96%
99.5%

(b) For a given level of confidence C, how does zcompare to t? Select ALL correct answers. i. For a given level of confidence C, zis larger than tfor some degrees of freedom and smaller than tfor some degrees of freedom. ii. For a given level of confidence C, zis always smaller than twith any degrees of freedom. iii. For a given level of confidence C, tgets closer to zwhile sample size increases. iv. For a given level of confidence C, tgets further ways from zwhile sample size in- creases.