A school pilot poll estimates $p=0.40$ for students who bike to school. For a 95 percent confidence interval with margin of error at most $0.03$ and $z^{\ast }=1.96$, how many students are needed?

A city pilot survey estimates $p=0.30$ for residents using a new trail. The planner wants a 95 percent confidence interval with margin of error at most $0.04$, using $z^{\ast }=1.96$. Find the smallest sample size.

A store pilot study estimates $p=0.65$ for customers who bring reusable bags. For a 90 percent confidence interval, margin of error at most $0.05$, and $z^{\ast }=1.645$, what sample size is needed?

A health clinic pilot estimates $p=0.20$ for patients requesting text reminders. For a 99 percent confidence interval, margin of error at most $0.025$, and $z^{\ast }=2.576$, what sample size is required?

A park pilot survey estimates $p=0.55$ for visitors who use the north entrance. With 95 percent confidence, $z^{\ast }=1.96$, and margin of error at most $0.04$, what is the minimum sample size?

A pilot poll estimates $p=0.12$ for students joining an after-school chess club. For a 90 percent confidence interval with margin of error at most $0.02$ and $z^{\ast }=1.645$, how many students should be surveyed?

A cafeteria survey has no prior estimate of $p$, the proportion favoring a salad bar. Using conservative $p=0.50$, a 95 percent interval, $z^{\ast }=1.96$, and margin of error at most $0.03$, what sample size is needed?

No pilot estimate is available for $p$, the proportion of bus riders using an app. Use conservative $p=0.50$, 95 percent confidence, $z^{\ast }=1.96$, and margin of error at most $0.04$. What is the minimum sample size?

A researcher has no prior estimate of $p$ for adults who recycle batteries. For 90 percent confidence, $z^{\ast }=1.645$, conservative $p=0.50$, and margin of error at most $0.05$, how many adults are needed?

A county has no prior estimate of $p$ for households with rain barrels. With conservative $p=0.50$, 95 percent confidence, $z^{\ast }=1.96$, and margin of error at most $0.025$, what sample size is required?

No prior estimate is known for $p$, the proportion of clinic patients using an online portal. For 99 percent confidence, $z^{\ast }=2.576$, conservative $p=0.50$, and margin of error at most $0.06$, find the sample size.

An engineer knows $\sigma =15$ minutes for part assembly time. For a 95 percent confidence interval for $\mu$ with margin of error at most $2$ minutes and $z^{\ast }=1.96$, what is the smallest sample size?

A lab knows $\sigma =8$ grams for soil sample mass measurements. To estimate $\mu$ with 95 percent confidence, $z^{\ast }=1.96$, and margin of error at most $1.5$ grams, how many measurements are needed?

A botanist knows $\sigma =12$ centimeters for plant heights. For a 99 percent confidence interval for $\mu$ with margin of error at most $3$ centimeters and $z^{\ast }=2.576$, determine the minimum sample size.

A factory knows $\sigma =20$ milliliters for bottle fill amounts. It wants a 90 percent confidence interval for $\mu$ with margin of error at most $4$ milliliters, using $z^{\ast }=1.645$. How many bottles are needed?

A climate lab knows $\sigma =5$ degrees Celsius for sensor readings. For a 95 percent confidence interval for $\mu$ with margin of error at most $0.8$ degrees Celsius and $z^{\ast }=1.96$, what sample size is required?

A farm knows $\sigma =3$ kilograms for crate weights. To estimate $\mu$ with 99 percent confidence, $z^{\ast }=2.576$, and margin of error at most $0.5$ kilograms, find the minimum sample size.

A survey of $n=600$ residents gives margin of error $0.04$ for $p$ at the 95 percent confidence level. At the same level and variability estimate, what sample size gives margin of error $0.02$?

A quality study with $n=350$ packages has margin of error $1.2$ grams for $\mu$. Keeping the same confidence level and $\sigma$, what sample size is needed for margin of error $0.6$ grams?

A transit poll with $n=900$ riders has margin of error $0.03$ for $p$. With the same confidence level and planning value of $p$, how large must the sample be for margin of error $0.015$?