Provide an appropriate response.
-Construct a $90 \%$ confidence interval for the population mean, $\mu$. Assume the population has a normal distribution. A sample of 15 randomly selected math majors has a grade point average of $2.86$ with a standard deviation of $0.78$.
A) $( 2.51,3.21 )$
B) $( 2.41,3.42 )$
C) $( 2.37,3.56 )$
D) $( 2.28,3.66 )$

Question

Quizplus · Accepted Answer

To construct a $90\%$ confidence interval for the population mean $\mu$, we use the formula: $\bar{x} \pm t_{\alpha/2} \cdot \frac{s}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $s$ is the sample standard deviation, $n$ is the sample size, and $t_{\alpha/2}$ is the t-score for $90\%$ confidence level with $n-1$ degrees of freedom. Given $\bar{x} = 2.86$, $s = 0.78$, and $n = 15$, and knowing the t-score for $90\%$ confidence level and 14 degrees of freedom is approximately $1.761$, the confidence interval is calculated as follows: $2.86 \pm 1.761 \cdot \frac{0.78}{\sqrt{15}}$, which results in approximately $(2.51, 3.21)$.

Provide an Appropriate Response 90%90 \%90% Confidence Interval for the Population Mean

Provide an Appropriate Response $90 \%$ Confidence Interval for the Population Mean