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how to fine this For a 95% confidence level and 14 degrees of freedom (15-1), the t-value is approximately 2.145.

Question

how to fine this For a 95% confidence level and 14 degrees of freedom (15-1), the t-value is approximately 2.145.

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Solution

To find the t-value for a 95% confidence level and 14 degrees of freedom, you can follow these steps:

  1. Identify the confidence level: In this case, the confidence level is 95%.

  2. Subtract the confidence level from 100% to find the alpha level: 100% - 95% = 5%.

  3. Divide the alpha level by 2: 5% / 2 = 2.5%. This is because the t-distribution is symmetrical around zero, and we are interested in the area in both tails of the distribution.

  4. Identify the degrees of freedom. The degrees of freedom are typically calculated as the sample size minus 1. In this case, the degrees of freedom are 14 (15 - 1).

  5. Use a t-distribution table to find the t-value that corresponds to the 2.5% alpha level (in the tail) and the specific degrees of freedom. In this case, the t-value is approximately 2.145.

Please note that the exact t-value can vary slightly depending on the specific t-distribution table used.

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