A company surveyed $250$ employees and found that $85$ of them prefer to work remotely. Construct a $95\%$ confidence interval for the proportion of all employees who prefer to work remotely.

A new antihistamine, Histarol, is known to cause dry mouth. In clinical trials, $200$ subjects received Histarol, and $50$ reported dry mouth. In a separate placebo group of $60$ subjects, $6$ reported dry mouth. Construct a $95\%$ confidence interval for the true proportion $p$ of placebo‐treated subjects who experience dry mouth.

A researcher wants to estimate the percentage of adults who can roll their tongue. The researcher assumes that $35\%$ of adults have this ability (based on prior studies). To estimate the true proportion with a margin of error of $4$ percentage points and a $99\%$ confidence level, what sample size is needed?

A pediatrician wants to estimate the percentage of new mothers who exclusively breastfeed their infants for at least six months. She needs to be $99\%$ confident that her survey estimate is within $2$ percentage points of the true rate. How many respondents must she include in her sample, assuming no prior estimate of the breastfeeding rate is available? What is wrong with polling randomly selected adult women instead of specifically targeting new mothers?

A recent survey reports a $95\%$ confidence interval for the percentage of small-business owners using cloud-based accounting software as . What is the best point estimate of the true percentage of small-business owners who use cloud accounting?

In a survey of $500$ registered voters, $185$ said they support a proposed environmental regulation. Find the point estimates for the population proportion $\hat{p}$ and $\hat{q}$.

A survey of $1500$ smartphone users found that $42\%$ use a password manager to store their login information. The survey reports a margin of error of $\pm 3\%$. Translate this information into a confidence interval and approximate the confidence level of the interval.