Estimating the Difference between Two Population Proportions Answers

In a statistics activity, students are asked to determine if there is a difference in the proportion of times that a spinning penny will land with tails up, and the proportion of times a spinning dime will land tails up. The students are instructed to spin the penny and the dime 30 times and record the number of times they land tails up. For one student, the penny lands tails side up 18 times, and the dime lands tails side up 20 times.Based on the 98% confidence interval, (–0.36, 0.22), is there evidence of a difference in proportions of tails side up for a penny and a dime?

In a statistics activity, students are asked to determine if there is a difference in the proportion of times that a spinning penny will land with tails up, and the proportion of times a spinning dime will land tails up. The students are instructed to spin the penny and the dime 30 times and record the number of times they land tails up. For one student, the penny lands tails side up 18 times, and the dime lands tails side up 20 times. Assuming the conditions for inference are met, what is the 98% confidence interval for the difference in proportions of tails side up for a penny and a dime?Find the z-table here.

A therapist wanted to determine if yoga or meditation is better for relieving stress. The therapist recruited 100 of her high-stress patients. Fifty of them were randomly assigned to take weekly yoga classes and the other 50 were assigned weekly meditation classes. After one month, 30 of the 50 patients in the yoga group reported less stress, and 35 of the 50 patients in the meditation group reported less stress. The therapist wants to construct a 95% confidence interval for the difference in proportions of patients experiencing stress relief after yoga and after meditation. Are the conditions for inference met?

A teacher has two large containers filled with blue, red, and green beads, and claims the proportions of red beads are the same in each container. Each student shakes the first container, selects 50 beads, counts the number of red beads, and returns the beads to the container. The student repeats this process for the second container. One student’s samples contained 13 red beads from the first container and 16 red beads from the second container.Based on the 95% confidence interval, (–0.24, 0.11), is the teacher’s claim justified?

The nutrition supervisor for a school district is considering adding a baked potato bar to the lunch menu for all the high school cafeterias. He wants to determine if there is a difference in the proportion of students who would purchase from the potato bar for two high schools, East and West. The cafeteria manager at each high school randomly surveys 90 students. At East High School, 63 of the students say they would purchase from the potato bar. At West High School, 58 students say they would. Assuming the conditions for inference have been met, what is the 99% confidence interval for the difference in proportion of students from the two schools who would purchase from the potato bar?Find the z-table here.

The owner of a popular coffee shop believes that customers who drink coffee are more likely to use their own cup than customers who drink espresso. Customers using their own cups get a 5% discount, which is displayed on the receipt. The owner randomly selects 50 receipts from all coffee purchases and 50 receipts from all espresso purchases. For coffee purchases, 24 receipts showed that the customer used their own cup. For espresso purchases, 18 receipts showed the customer used their own cup.Based on the 99% confidence interval, (–0.13, 0.37), is the coffee shop owner’s claim justified?

A teacher has two large containers filled with blue, red, and green beads. He wants his students to estimate the difference in the proportion of red beads in each container. Each student shakes the first container, randomly selects 50 beads, counts the number of red beads, and returns the beads to the container. The student repeats this process for the second container. One student sampled 13 red beads from the first container and 16 red beads from the second container. Assuming the conditions for inference are met, what is the 95% confidence interval for the difference in proportions of red beads in each container? Find the z-table here.

A therapist wanted to determine if yoga or meditation is better for relieving stress. The therapist recruited 100 of her high-stress patients. Fifty of them were randomly assigned to take weekly yoga classes, and the other 50 were assigned weekly meditation classes. After one month, 30 of the 50 patients in the yoga group reported less stress, and 35 of the 50 patients in the meditation group reported less stress.Based on the 95% confidence interval, (–0.29, 0.09), is there convincing evidence of a difference in the true proportions of patients experiencing stress relief in the yoga and meditation groups?

In a small town of 5,832 people, the mayor wants to determine if there is a difference in the proportion of voters ages 18–30 who would support an increase in the food tax, and the proportion of voters ages 31–40 who would support an increase in the food tax. An assistant to the mayor surveys 85 randomly chosen voters ages 18–30, and finds that 62 support the increase. A random sample of 70 voters ages 31–40 is also surveyed, and 56 support the increase. Assuming the conditions for inference have been met, what is the 99% confidence interval for the difference in proportions of voters who would support the increase in the food tax for the different age groups?Find the z-table here.

A local school board claims that there is a difference in the proportions of households with school-aged children that would support starting the school year a week earlier, and the proportion of households without school-aged children that would support starting the school year a week earlier. They survey a random sample of 40 households with school-aged children about whether they would support starting the school year a week earlier, and 30 households respond yes. They survey a random sample of 45 households that do not have school-aged children, and 25 respond yes.Based on the 90% confidence interval, (0.03, 0.36), is there convincing evidence of a difference in the true proportions of households, those with school-aged children and those without school-aged children, who would support starting school early?