the volleyball coach at a large high school wants to estimate the number of times players spike the ball…

Explanation:

Step1: Recall margin - of - error formula

The margin of error $E = z\cdot\frac{\sigma}{\sqrt{n}}$ for a confidence interval of the population mean (when population standard - deviation $\sigma$ is known), where $z$ is the z - score corresponding to the confidence level, $\sigma$ is the population standard deviation, and $n$ is the sample size. When $\sigma$ is unknown and we use the sample standard deviation $s$ instead, the formula for the margin of error for a t - distribution is $E = t\cdot\frac{s}{\sqrt{n}}$. In both cases, the margin of error is inversely proportional to the square root of the sample size $n$ and directly proportional to the critical value (either $z$ or $t$) which depends on the confidence level.

Step2: Analyze sample size effect

Increasing the sample size $n$ will decrease the margin of error because as $n$ gets larger, $\frac{1}{\sqrt{n}}$ gets smaller. So, using a smaller sample size (15 or 25 instead of 30) will increase the margin of error.

Step3: Analyze confidence - level effect

The critical value $z$ (or $t$) increases as the confidence level increases. For a 90% confidence interval, the critical value $z$ (or $t$) is smaller than for a 95% confidence interval, and the critical value for a 99% confidence interval is larger than for a 95% confidence interval. A smaller critical value will result in a smaller margin of error. So, constructing a 90% confidence interval (which has a smaller critical value compared to 95% and 99% confidence intervals) will decrease the margin of error.

Answer:

constructing a 90% confidence interval