Choose the one alternative that best completes the statement or answers the question.
-A group of 49 randomly selected parrots has a mean age of $22.4$ years with a population standard deviation of 3.8. Compute the $98 \%$ confidence interval for $\mu$.
A) $( 21.1,23.7 )$
B) $( 20.3,24.5 )$
C) $( 19.8,25.1 )$
D) $( 18.8,26.3 )$

Question

Quizplus · Accepted Answer

To calculate the 98% confidence interval for the mean age of the parrots, we use the formula for the confidence interval when the population standard deviation is known: $\bar{x} \pm Z \frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $Z$ is the Z-score corresponding to the confidence level, $\sigma$ is the population standard deviation, and $n$ is the sample size. For a 98% confidence level, the Z-score is approximately 2.33. Plugging in the given values: $22.4 \pm 2.33 \times \frac{3.8}{\sqrt{49}}$, we get the interval $(21.1, 23.7)$.

Choose the One Alternative That Best Completes the Statement or Answers