A group of 59 randomly selected students have a mean score of $29.5$ with a standard deviation of $5.2$ on a placement test. What is the $90 \%$ confidence interval for the mean score, $\mu$, of all students taking the test?
A) $28.2

Question

A group of 59 randomly selected students have a mean score of $29.5$ with a standard deviation of $5.2$ on a placement test. What is the $90 \%$ confidence interval for the mean score, $\mu$, of all students taking the test?
A) $28.2 < \mu < 30.8$
B) $28.4 < \mu < 30.6$
C) $27.8 < \mu < 31.2$
D) $27.9 < \mu < 31.1$

Quizplus · Accepted Answer

The 90% confidence interval is calculated using the formula: $\bar{x} \pm z \times \frac{s}{\sqrt{n}}$, where $\bar{x} = 29.5$, $s = 5.2$, $n = 59$, and $z$ for 90% confidence is approximately 1.645. This gives the interval $28.4 < \mu < 30.6$.

A Group of 59 Randomly Selected Students Have a Mean 29.529.529.5

A Group of 59 Randomly Selected Students Have a Mean $29.5$