a school nurse would like to estimate the true mean amount of sleep that students at the high school get per…

Explanation:

Step1: Recall confidence - interval formula

The formula for a confidence interval for the population mean (when the population standard - deviation $\sigma$ is known) is $\bar{x}\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$, and the width of the confidence interval $W = 2z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $z_{\alpha/2}$ is the z - score corresponding to the level of confidence, $\sigma$ is the population standard deviation, and $n$ is the sample size.

Step2: Analyze the effect of each option

• Selecting another sample: This may change the sample mean and other sample - related statistics, but it does not systematically decrease the width of the interval.
• Decreasing the sample size $n$: From the formula $W = 2z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$, when $n$ decreases, $\frac{\sigma}{\sqrt{n}}$ increases, and thus the width $W$ increases.
• Increasing the confidence level: As the confidence level increases, the value of $z_{\alpha/2}$ increases. For example, for a 90% confidence level, $z_{\alpha/2}\approx1.645$, and for a 95% confidence level, $z_{\alpha/2}\approx1.96$. Since $W = 2z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$, an increase in $z_{\alpha/2}$ will increase the width $W$.
• Decreasing the confidence level: When the confidence level decreases, the value of $z_{\alpha/2}$ decreases. Since $W = 2z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$, a decrease in $z_{\alpha/2}$ will decrease the width $W$.

Answer:

decreasing the confidence level