Use the confidence level and sample data to find a confidence interval for estimating the population µ. Round your answer to the same number of decimal places as the sample mean.
-A group of 64 randomly selected students have a mean score of $38.6$ with a standard deviation of $4.9$ on a placement test. What is the $90 \%$ confidence interval for the mean score, $\mu$, of all students taking the test?
A) $37.4

Question

Use the confidence level and sample data to find a confidence interval for estimating the population µ. Round your answer to the same number of decimal places as the sample mean.
-A group of 64 randomly selected students have a mean score of $38.6$ with a standard deviation of $4.9$ on a placement test. What is the $90 \%$ confidence interval for the mean score, $\mu$, of all students taking the test?
A) $37.4 < \mu < 39.8$
B) $37.2 < \mu < 40.0$
C) $37.6 < \mu < 39.6$
D) $37.0 < \mu < 40.2$

Quizplus · Accepted Answer

The 90% confidence interval is calculated using the formula: $\bar{x} \pm z \times \frac{\sigma}{\sqrt{n}}$. Here, $\bar{x} = 38.6$, $\sigma = 4.9$, $n = 64$, and the z-value for 90% confidence is approximately 1.645. The interval is $38.6 \pm 1.645 \times \frac{4.9}{\sqrt{64}}$, which simplifies to $37.6 < \mu < 39.6$.

Use the Confidence Level and Sample Data to Find a Confidence