Help Determine the t-value in each of the cases Click the icon to view the table
ID: 2948514 • Letter: H
Question
Help Determine the t-value in each of the cases Click the icon to view the table of areas under the -distribution. (a) Find the t-value such that the area in the right tail is 0.005 with 11 degrees of freedom. (Round to three decimal places as needed.) (b) Find the t-value such that the area in the right tail is 0.02 with 20 degrees of freedom. (Round to three decimal places as needed.) (e) Find the t-value such that the area left of the t-value is 0.25 with 20 degrees of freedom. [Hint: Use symmetry] ? (Round to three decimal places as needed.) (d) Find the critical t-value that corresponds to 70% confidence. Assume 23 degrees of freedom. (Round to three decimal places as needed) Enter your answer in each of the answer boxes. 06/29/1810.3 Formative Assessment 11:59pmExplanation / Answer
This is to be done directly from the t distribution tables. The values are computed here as:
a) P( t11 > k ) = 0.005
P( t11 < k ) = 1 - 0.005 = 0.995
From tables, we get: P( t11 < 3.106 ) = 0.995
Therefore 3.106 is the required t value here.
b) Similar way to above case,
P( t20 < 2.197) = 0.98
P( t20 > 2.197) = 0.02
Therefore 2.197 is the required t value here.
c) From t distribution tables, we get:
P( t20 < -0.687) = 0.25
Therefore - 0.687 is the required t score here.
d) For 70% confidence, we need to find k such that:
P( -k < t < k ) = 0.7
Therefore due to symmetry,
P( t < k) = 0.7 + 0.3/2 = 0.85
From tables, we get:
P( t23 < 1.060) = 0.85
Therefore 1.060 is the required t score here.
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