Provide an appropriate response.
-Construct a $95 \%$ confidence interval for the population mean, $\mu$. Assume the population has a normal distribution. A sample of 25 randomly English majors has a mean test score of $81.5$ with a standard deviation of $10.2$.
A) $( 77.29,85.71 )$
B) $( 56.12,78.34 )$
C) $( 66.35,69.89 )$
D) $( 87.12,98.32 )$

Question

Quizplus · Accepted Answer

To construct a 95% confidence interval for the population mean, use the formula: $\bar{x} \pm z\frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $z$ is the z-score corresponding to the confidence level (for 95%, $z = 1.96$), $\sigma$ is the standard deviation, and $n$ is the sample size. Plugging in the given values: $81.5 \pm 1.96\frac{10.2}{\sqrt{25}}$ results in the interval $(77.29, 85.71)$.

Provide an Appropriate Response 95%95 \%95% Confidence Interval for the Population Mean

Provide an Appropriate Response $95 \%$ Confidence Interval for the Population Mean