Questions: What is the value of the t score for a 99.8% confidence interval if we take a sample of size 5?

Solution Steps

To find the $t$ score for a $99.8\%$ confidence interval with a sample size of 5, we need to use the t-distribution table or a statistical function. The degrees of freedom (df) will be the sample size minus one. For a sample size of 5, df = 4. We then look up the $t$ score that corresponds to the $99.8\%$ confidence level.

For a sample size of \( n = 5 \), the degrees of freedom (df) is calculated as: \[ df = n - 1 = 5 - 1 = 4 \]

The confidence level given is \( 99.8\% \), which can be expressed as: \[ \alpha = 1 - 0.998 = 0.002 \]

To find the t-score corresponding to a \( 99.8\% \) confidence interval with \( df = 4 \), we look for the critical value at \( \frac{1 + 0.998}{2} = 0.999 \). The calculated t-score is: \[ t = 7.1732 \]

Final Answer