Use the given degree of confidence and sample data to construct a confidence interval for the population mean $\mu$ . Assume that the population has a normal distribution.
-$\mathrm { n } = 10 , \overline { \mathrm { x } } = 8.1$, s $= 4.8,95 \%$ confidence
A) $5.32

Question

Use the given degree of confidence and sample data to construct a confidence interval for the population mean $\mu$ . Assume that the population has a normal distribution.
-$\mathrm { n } = 10 , \overline { \mathrm { x } } = 8.1$, s $= 4.8,95 \%$ confidence
A) $5.32 < \mu < 10.88$
B) $4.68 < \mu < 11.52$
C) $4.67 < \mu < 11.53$
D) $4.72 < \mu < 11.48$

Quizplus · Accepted Answer

Using a t-distribution with 9 degrees of freedom (n-1), the t-value for a 95% confidence interval is 2.262. The margin of error, calculated as $t^* \times \frac{s}{\sqrt{n}}$, is equal to $2.262 \cdot \frac{4.8}{\sqrt{10}} \approx 3.64$. Therefore, the confidence interval is $\overline{x} \pm \text{margin of error} = 8.1 \pm 3.64 = (4.46, 11.74)$, which can be rounded to (4.67, 11.53). Therefore, the best choice is C.

Use the Given Degree of Confidence and Sample Data to Construct