2. Critical Values from the t-table (Table D). (a) Accurate to the nearest 3 dec

Question

2. Critical Values from the t-table (Table D). (a) Accurate to the nearest 3 decimal places, what is the critical value (t or z ) that corresponds to the given confidence levels and degrees of freedom. Fill in the following table with the appropriate critical values (use the rule discussed in class when the exact df are not listed in Table D).

Please briefly answer b-d.

(b) [Free Response.] For a given level of confidence C, how does t compare to z ? Note that this holds true for all degrees of freedom values as long as they are finite.

(c) [Free Response.] For a given level of confidence C, how does t change compared to z as the df increase?

(d) [Free Response.] For a given df value, how does t change as C increases?

Confidence level unknown (r) known (2) 50% 70% 90% 95%

Explanation / Answer

from above below are the critical vales:

b)   For a given level of confidence C, t is greater then compare to z

c) For a given level of confidence C, t approaches z as the df increase

d)

For a given df value t increases as C increases

t z confidence level df=17 df=40 df=75 50% 0.689 0.681 0.678 0.674 70% 1.069 1.050 1.044 1.036 90% 1.740 1.684 1.665 1.645 95% 2.110 2.021 1.992 1.960

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