Confidence Intervals

Problem 1: Healthcare for all American

A Gallup poll found that 493 of 1050 adult Americans believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage.

1.What is the sample in this study? What is the population of interest?

2.What is the variable of interest in this study? Is it qualitative or quantitative?

3.Based on the results of this study, obtain a point estimate for the proportion of adult Americans who believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage.

4.Explain why the point estimate in #3 is a statistic? What is it a random variable?

5.Construct and interpret a 90% confidence interval for the proportion of adult Americans who believe it is the responsibility of the federal government to make sure all Americans have healthcare coverage.

6.Name two things that might be done to increase the precision of the confidence interval?

Problem 2: Speeding in a construction zone

A group of Brigham Young UniversityIdaho students collected data on the speed of vehicles traveling through a construction zone on a state highway, where the speed was 25 mph. The recorded speed (in mph) of 14 randomly selected vehicles is given below:

20,24,27,28,29,30,32,33,34,36,38,39,40,40

1.Assuming speeds are approximately normally distributed, construct a 95% confidence interval for the true mean speed of drivers in this construction zone. Interpret the interval.

2.Construct a 99% confidence interval for the true mean speed of drivers in this construction zone. Interpret the interval.

3.Compare the widths of the 95% and 99% confidence intervals.

4.What conclusions do you draw about the speeds people drive in this construction zone?