Preparing to Estimate a Population Proportion Answers

In a small town of 5,832 people, the mayor wants to determine the proportion of voters who would support an increase to the food tax. An assistant to the mayor decides to survey 1,000 randomly chosen people to construct a 90% confidence interval for the true proportion of people who would support the increase in food tax. Of the sample, 363 people say they would support the increase. Are the conditions for inference met?

A computer company wants to determine the proportion of defective computer chips from a day’s production. A quality control specialist takes a sample of 100 chips from the first hour of production and determines that there are 12 defective chips. He wants to construct a 90% confidence interval for the true proportion of defective chips from a day’s production. Are the conditions for inference met?

What is the z* critical value for constructing an 88% confidence interval for a proportion?Find the z-table here.

A student believes that a certain number cube is unfair and is more likely to land with a six facing up. The student rolls the number cube 45 times and the cube lands with a six facing up 12 times. Assuming the conditions for inference have been met, what is the 99% confidence interval for the true proportion of times the number cube would land with a six facing up?

What is the z* critical value for constructing a 99% confidence interval for a proportion?Find the z-table here.

A local school board wants to determine the proportion of households in the district that would support starting the school year a week earlier. They ask a random sample of 100 households whether they would support starting the school year a week earlier, and 43 households responded that they would. The school board plans to construct a 95% confidence interval for the true proportion of households that would support starting the school year a week earlier. Are the conditions for inference met?

A computer company wants to determine the proportion of defective computer chips from a day’s production. A quality control specialist takes a random sample of 100 chips from the day’s production and determines that there were 12 defective chips. He wants to construct a 90% confidence interval for the true proportion of defective chips from the day’s production. Are the conditions for inference met?

At a local college, an admissions officer wants to survey the incoming class of 500 first-year students concerning their preference of major. The officer randomly selects 100 of them to complete the survey, and finds that 45 are planning to major in liberal arts. The admissions officer uses the data to construct a 95% confidence interval for the proportion of first-year students who are planning on majoring in liberal arts. Are the conditions for inference met?

A student wants to survey the sophomore class of 200 students about whether the school should require uniforms. A random sample of 18 sophomores is surveyed and asked whether they support the school adopting uniforms, and three students said yes. The student wants to construct a 95% confidence interval for the proportion of sophomores who favor the adoption of uniforms. Are the conditions for inference met?

What is the z* critical value for constructing a 94% confidence interval for a proportion?Find the z-table here.