Unit 6: Inference for Categorical Data: Proportions

A random sample of 400 registered voters found that 224 support a proposed ballot measure.

A company claims that 30% of its customers are repeat buyers. A market researcher suspects the rate is lower. In a random sample of 250 customers, 62 are repeat buyers.

A study compared flu vaccination rates between two age groups. Among 500 adults aged 18–49, 175 were vaccinated. Among 400 adults aged 50+, 220 were vaccinated.

A pharmaceutical company tests a new drug to reduce headache frequency. In a randomized experiment, 120 of 200 patients given the drug reported improvement, compared to 85 of 200 patients given a placebo.

A consumer group claims that fewer than 25% of fast-food meals meet nutritional guidelines. In a random sample of 300 meals from various restaurants, 60 met the guidelines ([math]).

A researcher plans to test [math] vs [math] at [math] using a random sample.

A news organization polls 1,200 likely voters and finds [math] support a candidate. The reported margin of error is [math] at 95% confidence.

A 95% confidence interval for the proportion of adults who exercise regularly is [math], based on a random sample of 600 adults.

An airport claims that 85% of flights depart on time. A watchdog group collects data on 500 randomly selected flights and finds 405 departed on time ([math]).

Two factories produce light bulbs. Factory 1 has a 4% defect rate; Factory 2 has a 6% defect rate. Random samples of 500 from Factory 1 and 400 from Factory 2 are tested.