A survey of 500 shoppers gives a 90% confidence interval for the proportion using a loyalty card, with margin of error 0.035. The same data are used for a 99% interval. What happens to the margin of error?

A clinic reports a 99% confidence interval for mean wait time with margin of error 4.8 minutes. The same sample data are reported at 95% confidence instead. What happens to the margin of error?

Two reports use the same random sample of 300 soil plots and the same sample standard deviation. One gives a 90% interval and one gives a 95% interval for mean nitrogen level. Which report has the larger margin of error?

A school survey gives a 95% interval for the proportion of students who bike to school, with margin of error 0.040. If only the confidence level is raised to 98%, what happens to the interval width?

A city survey of 800 residents gives a 95% interval for the proportion supporting a bike lane, with margin of error 0.028. The same data are reported at 90% confidence. What happens to the margin of error?

A hospital audit uses the same 240 patient records to make 80% and 95% confidence intervals for a mean recovery time. The sample standard deviation is the same. Which interval has the smaller margin of error?

A senior class poll uses one sample of 250 students. Interval A is 92% confidence and interval B is 98% confidence for the same proportion. How do the margins of error compare?

A lab changes only the confidence level for a mean temperature interval from 99% to 90%, keeping the sample and variability unchanged. What happens to the interval?

A random sample of 400 seedlings gives a 95% interval for mean height with margin of error 1.2 cm. A second study uses the same confidence level and standard deviation but samples 1,600 seedlings. What is its margin of error?

A poll of 900 voters has a margin of error of 3.2 percentage points at one confidence level. Another poll uses the same level and variability but only 225 voters. What is its margin of error?

A factory sample of 100 bolts gives a 95% interval for mean diameter with margin of error 0.40 mm. The same method samples 400 bolts with the same standard deviation. What is the new margin of error?

A lake study with 625 fish has a margin of error of 1.6 cm for mean length. A new study keeps the same confidence level and standard deviation but samples 2,500 fish. What is the margin of error?

A transit study samples 121 trips and has a margin of error of 2.2 minutes for mean delay. A follow-up samples 484 trips with the same confidence level and variability. What is the margin of error?

A school laptop survey of 1,600 students has a margin of error of 0.025. A smaller survey uses 400 students with the same confidence level and variability. What is the smaller survey's margin of error?

A wildlife survey has margin of error 0.100 with 500 nests. If researchers double the sample size to 1,000 nests and keep the same confidence level and variability, what is the margin of error, rounded to three decimals?

A nutrition study samples 200 meals and has a margin of error of 1.4 g for mean sugar. A new study samples 800 meals with the same confidence level and standard deviation. What is the margin of error?

Two 95% intervals for mean plant growth use samples of 180 plants each. Sample A has standard deviation 3 cm, and sample B has standard deviation 8 cm. Which interval has the larger margin of error?

A bottling process has margin of error 0.30 mL when the population standard deviation is 1.2 mL. If only the standard deviation increases to 2.4 mL, what is the new margin of error?

Two classes have the same sample size and confidence level for intervals estimating mean quiz score. Class A has standard deviation 5 points, and class B has standard deviation 10 points. Which interval is narrower?

A sensor study keeps the same sample size and 95% confidence level. After recalibration, the sample standard deviation falls from 0.8 g to 0.4 g. What happens to the margin of error?

Two greenhouse studies use 150 days of data and 95% confidence. One has temperature standard deviation 2 °C, and the other has 6 °C. What explains which interval is wider?

A coach estimates mean race time for two teams using the same sample size and confidence level. Team Red has standard deviation 0.5 seconds, and Team Blue has 1.5 seconds. Which margin of error is larger?

A study reports a 95% confidence interval from 12.4 to 17.6 kilograms for mean calf mass gain. What is the margin of error of this interval?

A poll reports a confidence interval from 0.41 to 0.49 for a population proportion. What is the margin of error?

A transit agency reports a confidence interval from 23.8 to 29.2 minutes for mean commute time. What is the margin of error?

A health study reports a confidence interval from 156 to 168 cm for mean adult height in a sample's population. What is the margin of error?

A dairy report gives a confidence interval from 5.6 to 7.4 liters for mean daily milk production per goat. What is the margin of error?

A weather station reports a confidence interval from 18.3 °C to 19.1 °C for mean morning temperature. What is the margin of error?

A city reports a 95% interval from 42% to 50% for bus riders, with point estimate 46%. Same data are reported at 90%. What happens to the point estimate and endpoints?

A clinic's 95% interval for mean wait time is too wide. The clinic can change only the number of patients sampled, while confidence level and variability stay the same. What change narrows the interval?

A researcher has a 95% interval for mean sleep time and cannot collect more data or change variability. What confidence level would make the interval narrower?

A packaging lab keeps the same sample size and 95% confidence level for mean mass. What process change would narrow the interval?

A lake study's point estimate is 7.0 mg/L, with current margin of error 1.2 mg/L. A new method narrows the margin of error to 0.5 mg/L with the same point estimate. What interval endpoints result?

A farm reports a point estimate of 28 cm and margin of error 3 cm for mean plant height. Lowering the confidence level makes the margin of error 2 cm. How do the endpoints change?

A researcher wants to cut the margin of error of a 95% interval to one third of its current value, with confidence level and population standard deviation unchanged. By what factor must the sample size be multiplied?

A survey team wants the margin of error to be one half of its current value, keeping the confidence level and variability unchanged. By what factor must the sample size be multiplied?

A quality-control team wants the margin of error for mean fill amount to be one fourth as large, with the same confidence level and standard deviation. What sample-size multiplier is needed?

A park survey wants the margin of error to be two thirds of its current value, with confidence level and variability unchanged. By what factor should the sample size be multiplied?

A machine study has margin of error 5.0 mm. Engineers want a margin of error of 1.0 mm, keeping confidence level and variability unchanged. By what factor must the sample size be multiplied?

A statewide poll has margin of error 1.8 percentage points. Pollsters want 0.6 percentage points with the same confidence level and variability. By what factor must the sample size be multiplied?