## Contruct A 98% Confidence Interval

The text discusses the use of t-values and critical values in statistics. It mentions that for sample sizes smaller than 30, t-values are used instead of z-scores and the t-value depends on the degrees of freedom. It presents a table of critical values for confidence levels of 80%, 90%, 95%, 98%, and 99% for different degrees of freedom. It also shows a table for t-values at different confidence levels and degrees of freedom. The text explains how to find the critical t-value for a given confidence level and sample size, with example problems provided. It also discusses the use of one-tail and two-tail probabilities in finding critical values. Overall, the text focuses on the importance of understanding and using critical values in statistical analysis.

The t-score for a 98% confidence level and 8 degrees of freedom is approximately 3.355.

Using this information, we can calculate the 98% confidence interval for the mean nicotine content of the new brand of cigarettes. Plugging in the given values: [ 24.3 \pm 3.355 \left( \frac{2.6}{\sqrt{9}} \right) ] [ 24.3 \pm 3.355 \times \frac{2.6}{3} ]

By performing this calculation, we can obtain the 98% confidence interval for the mean nicotine content of the new brand of cigarettes.

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