Use the confidence level and sample data to find a confidence interval for estimating the population µ.
-A random sample of 144 full-grown lobsters had a mean weight of 18 ounces and a standard deviation of $2.9$ ounces. Construct a 98 percent confidence interval for the population mean $\mu$.
A) $16

Question

Use the confidence level and sample data to find a confidence interval for estimating the population µ.
-A random sample of 144 full-grown lobsters had a mean weight of 18 ounces and a standard deviation of $2.9$ ounces. Construct a 98 percent confidence interval for the population mean $\mu$.
A) $16 < \mu < 18$
B) $17 < \mu < 20$
C) $18 < \mu < 20$
D) $17 < \mu < 19$

Quizplus · Accepted Answer

To construct a 98% confidence interval for the population mean $\mu$, we use the formula for the confidence interval: $\bar{x} \pm z\frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $z$ is the z-score corresponding to the confidence level, $\sigma$ is the standard deviation, and $n$ is the sample size. Given $\bar{x} = 18$, $\sigma = 2.9$, and $n = 144$, for a 98% confidence level, the z-score is approximately 2.33. Plugging in the values: $18 \pm 2.33 \times \frac{2.9}{\sqrt{144}} = 18 \pm 0.45$, which gives us the interval $17.55 < \mu < 18.45$, rounding to whole numbers doesn't match exactly but the closest and correct option is $17 < \mu < 19$.

Use the Confidence Level and Sample Data to Find a Confidence