Estimating a Population Proportion Answers

A scientist wants to sample fish from a large aquarium to estimate the true proportion of striped fish. How many fish are required for a random sample to obtain a margin of error of at most 0.06 with 95% confidence?Find the z-table here.

A politician estimates that 61% of his constituents will vote for him in the coming election. How many constituents are required for a random sample to obtain a margin of error of at most 0.03 with 95% confidence?Find the z-table here.

Katie selects a simple random sample of 25 students at her large school and finds that 5 of them are planning to try out for the soccer team next year. She wants to construct a confidence interval for p = the proportion of all students at her school who plan to try out for the soccer team next year, but she realizes she hasn’t met all the conditions for constructing the interval. Which condition for this procedure has she failed to meet?

A researcher takes a random sample of 2,496 drivers and finds that 1,603 put their phone in "drive mode” to not be distracted while driving. A 90% confidence interval for the proportion of drivers who use "drive mode” on their phones is (0.626, 0.658). Which statement correctly interprets the interval?

A recent report stated that over half of food delivery drivers eat some of the food they are delivering. A 95% confidence interval for the true proportion of food delivery drivers who eat some of the food they are delivering is (0.398, 0.706). Is it reasonable to believe more than half of food delivery drivers eat some of the food they are delivering?

The proportion of customers who pay their credit card bill on time is 84%. Administrators at a large university believe less than 84% of the students enrolled pay their credit card bill on time. The 95% confidence interval for the true proportion of students enrolled in this university who pay their credit card bill on time is (0.791, 0.839). Is it reasonable to believe the true proportion of students at this university who pay their credit card bill on time is less than 84%?

Ellen’s mom thinks the local weather forecaster correctly predicts the weather 85% of the time, but Ellen thinks it is less than that. The 95% confidence interval for the true proportion of correct forecasts by this weather forecaster is (0.796, 0.862). Is it reasonable to believe the true proportion of times this weather forecaster correctly predicts the weather is less than 85%?

A technology company claims that 13% of customers who call the help desk cannot log in because they have their keyboard on caps lock, which blocks the log in process due to password case sensitivity. Brian, a help desk worker at this company, thinks this proportion is higher. The 95% confidence interval for the true proportion of customers who cannot log in due to caps lock is (0.128, 0.185). Is it reasonable to believe the true proportion of customers who cannot log in due to caps lock is greater than 13%?

A producer of 10-ounce bags of pretzels claims that less than 7% of the pretzels in each bag are broken. The 95% confidence interval for the true proportion of broken pretzels in the 10-ounce bags produced by this company is (0.036, 0.067). Is it reasonable to conclude that less than 7% of pretzels in each bag are broken?

A recent study estimated that 68% of US adults enjoy reading a book while relaxing. How many adults are required for a random sample to obtain a margin of error of at most 0.05 with 90% confidence?Find the z-table here.