Questions: Determine the t-value in each of the cases. (a) Find the t-value such that the area in the right tail is 0.02 with 24 degrees of freedom. 2.172 (Round to three decimal places as needed.) (b) Find the t-value such that the area in the right tail is 0.05 with 19 degrees of freedom. 1.729 (Round to three decimal places as needed.) (c) Find the t-value such that the area left of the t-value is 0.25 with 30 degrees of freedom. (Round to three decimal places as needed.)

Determine the t-value in each of the cases.
(a) Find the t-value such that the area in the right tail is 0.02 with 24 degrees of freedom.
2.172 (Round to three decimal places as needed.)
(b) Find the t-value such that the area in the right tail is 0.05 with 19 degrees of freedom.
1.729 (Round to three decimal places as needed.)
(c) Find the t-value such that the area left of the t-value is 0.25 with 30 degrees of freedom. (Round to three decimal places as needed.)
Transcript text: Determine the $t$-value in each of the cases. (a) Find the $t$-value such that the area in the right tail is 0.02 with 24 degrees of freedom. 2.172 (Round to three decimal places as needed.) (b) Find the $t$-value such that the area in the right tail is 0.05 with 19 degrees of freedom. 1.729 (Round to three decimal places as needed.) (c) Find the $t$-value such that the area left of the $t$-value is 0.25 with 30 degrees of freedom. (Round to three decimal places as needed.)
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Solution

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Solution Steps

Step 1: Identify the area under the curve and degrees of freedom

Given area: 0.02, Degrees of freedom: 24

Step 2: Calculate the $t$-value using the t-distribution

Using the t-distribution, the $t$-value is calculated as 2.172

Final Answer:

The $t$-value(s) for the given area under the curve with 24 degrees of freedom is 2.172.

Step 1: Identify the area under the curve and degrees of freedom

Given area: 0.05, Degrees of freedom: 19

Step 2: Calculate the $t$-value using the t-distribution

Using the t-distribution, the $t$-value is calculated as 1.729

Final Answer:

The $t$-value(s) for the given area under the curve with 19 degrees of freedom is 1.729.

Step 1: Identify the area under the curve and degrees of freedom

Given area: 0.25, Degrees of freedom: 30

Step 2: Calculate the $t$-value using the t-distribution

Using the t-distribution, the $t$-value is calculated as 0.683

Final Answer:

The $t$-value(s) for the given area under the curve with 30 degrees of freedom is 0.683.

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