Sample size $= 256$, sample mean $= 40$, sample standard deviation $= 13$
What is the $95 \%$ confidence interval for the population mean?
A) $39.2

Question

Sample size $= 256$, sample mean $= 40$, sample standard deviation $= 13$
What is the $95 \%$ confidence interval for the population mean?
A) $39.2 < \mu < 40.8$
B) $38.4 < \mu < 41.6$
C) $39.9 < \mu < 40.1$
D) $8 < \mu < 18$

Quizplus · Accepted Answer

The 95% confidence interval is calculated using the formula: $\bar{x} \pm z \times \frac{s}{\sqrt{n}}$, where $z$ is the z-score for 95% confidence (1.96), $\bar{x}$ is the sample mean, $s$ is the sample standard deviation, and $n$ is the sample size. Plugging in the values: $40 \pm 1.96 \times \frac{13}{\sqrt{256}}$ gives the interval $38.4 < \mu < 41.6$.

Sample Size =256= 256=256 , Sample Mean =40= 40=40 , Sample Standard Deviation

Sample Size $= 256$ , Sample Mean $= 40$ , Sample Standard Deviation