Provide an appropriate response.
-Construct a $90 \%$ confidence interval for the population mean, $\mu$. Assume the population has a normal distribution. In a recent study of 22 eighth graders, the mean number of hours per week that they played video games was $19.6$ with a standard deviation of $5.8$ hours.
A) $( 17.47,21.73 )$
B) $( 18.63,20.89 )$
C) $( 5.87,7.98 )$
D) $( 19.62,23.12 )$

Question

Quizplus · Accepted Answer

To construct a 90% confidence interval for the population mean, 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 the desired confidence level with $n-1$ degrees of freedom. Given $\bar{x} = 19.6$, $s = 5.8$, and $n = 22$, and knowing the distribution is normal, we can calculate the interval. The correct interval, given these values and a 90% confidence level, is $(17.47, 21.73)$, which matches choice A.

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

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