To find the critical t value for a confidence level of 80% with a sample size of 25, you can follow these steps:
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Determine the degrees of freedom (df): This is calculated as the sample size minus 1. For a sample size of 25: \[ df = n - 1 = 25 - 1 = 24 \]
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Determine the critical value for the t-distribution: Since the confidence level is 80%, the remaining percentage in the two tails of the distribution is \(100% - 80% = 20%\). Since it is a two-tailed test, you will need to divide this by 2: \[ \alpha = \frac{20%}{2} = 10% = 0.10 \]
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Look up the critical t value: You can use a t-distribution table or statistical software to find the critical t value for \(df = 24\) at a significance level of \(0.10\) for each tail.
If you look it up in a t-table for \(df = 24\):
- The critical t value at a significance level of \(0.10\) in each tail (for a two-tailed test) is approximately \(t_{0.10, 24} \approx 1.318\).
Thus, the critical t value for a confidence level of 80% with a sample size of 25 is approximately ±1.318.