A company that produces computers recently tested the battery in its latest laptop in six separate trials. The battery lasted 8.23,7.89,8.14,8.25,8.30, and 7.95 hours before burning out in each of the tests. Assuming the battery duration is normally distributed, construct a 95% confidence interval for the mean battery life in the new model.
A) [7.9490, 8.3044]
B) [7.9575, 8.2959]
C) [7.9873, 8.2661]
D) [7.9912, 8.2622]

Question

Quizplus · Accepted Answer

To construct a 95% confidence interval for the mean battery life, first calculate the sample mean ($\bar{x}$) and the sample standard deviation (s). The sample mean is $\bar{x} = \frac{8.23 + 7.89 + 8.14 + 8.25 + 8.30 + 7.95}{6} = 8.127$. The sample standard deviation can be calculated using the formula $s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}}$, which gives $s \approx 0.152$. For a 95% confidence interval and a sample size of 6, we use the t-distribution with $n-1 = 5$ degrees of freedom. The t-value for 95% confidence and 5 degrees of freedom (from t-tables or calculators) is approximately 2.571. The confidence interval is calculated as $\bar{x} \pm t \cdot \frac{s}{\sqrt{n}}$, which gives $[7.9490, 8.3044]$.

A Company That Produces Computers Recently Tested the Battery in Its