Narrow a confidence interval for a mean

Suppose you draw a simple random sample with $n = 100$ and observe a sample mean of $100$. The current 95% confidence interval for the population mean is $100 \pm 10$, and a PM considers that interval too wide. a) If you raise $n$ to $10{,}000$ while the sample standard deviation $s$ stays the same, work out the new 95% CI half-width exactly and describe the $1/\sqrt{n}$ scaling. b) Keeping $n$ fixed, name and justify at least four concrete levers that can shrink the CI—for example, alter the confidence level $\alpha$, lower variance through paired designs/blocking/stratification, cut measurement noise, or transform the outcome—and explain the trade-offs or risks of each. c) Under what conditions is narrowing the CI by increasing $\alpha$ misleading, and how would you explain that risk to a non-statistical audience?

Overview: This question tests grasp of confidence intervals, how interval width depends on sample size, variance-reduction methods, the effect of changing the confidence level, and the ability to convey statistical risk and design trade-offs.