Question

Determine the? t-value in each of the cases. LOADING...

?(a) Find the? t-value such that the area in the right tail is 0.25 0.25 with 25 25 degrees of freedom. nothing ?(Round to three decimal places as? needed.) ?

(b) Find the? t-value such that the area in the right tail is 0.025 0.025 with 21 21 degrees of freedom. nothing ?(Round to three decimal places as? needed.)

?(c) Find the? t-value such that the area left of the? t-value is 0.20 0.20 with 20 20 degrees of freedom.? [Hint: Use? symmetry.] nothing ?(Round to three decimal places as? needed.) ?

(d) Find the critical? t-value that corresponds to 80 80?% confidence. Assume 13 13 degrees of freedom. nothing ?(Round to three decimal places as? needed.)

Answer 1

• That is, the percentage of the distribution that lies above the values given in the table. The number on the left of each row is the degrees of freedom. The table only gives the upper tail percentage points. This is because the t-distribution is symmetrical about zero.
• a)Here To find the value a such that area in the right t_(0.025,25) we look along the 25 degrees of freedom row until we reach the 2.5% column. The value is 2.060
• B)Similary,To find the value a such that area in the right t_(0.025,21) we look along the 21 degrees of freedom row until we reach the 2.5% column. The value is 2.080.
• c)To find the value a such that area in the left t_(0.2,20) (since t distribution is symetric we will use the same way ) we look along the 21 degrees of freedom row until we reach the 20% column -0.8600
• d)The critical value for 80% confidence interval is given by
• The critical value at Z_a/2=>Z_0.20/2=Z_0.10 for 13 degrees of freedom is given by 1.350
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