In a survey of 1,200 randomly selected adults, it was found that 702 of those surveyed said they would prefer balancing the United States government's budget by raising taxes.
1. Suppose that the survey used a simple random sample. A 95% confidence interval for the proportion of all adults who prefer balancing the budget by raising taxes is:
a. 0.585 ± 0.0004
b. 0.585 ± 0.014
c. 0.585 ± 0.023
d. 0.585 ± 0.028
2. A member of Congress thinks that 95% confidence isn't high enough. He wants to be 99% confident. How would the margin of error of a 99% confidence interval, based on the same sample of 1200 adults, compare with the 95% interval you found in the previous question?
a. It would be the same because the sample is the same.
b. It would be smaller because it omits only 1% of the possible samples instead of 5%.
c. It would be larger because higher confidence requires a larger margin of error.
3. Another member of Congress is satisfied with 95% confidence, but she wants a smaller margin of error. How can we get a smaller margin of error and still be at 95% confidence?
a. Take a larger random sample because larger samples result in smaller margins of error.
b. Take a smaller random sample because smaller samples result in smaller margins of error.
c. Take many random samples each with 1,200 adults, and choose the one that has the smallest margin of error.
4. The Gallup Poll surveyed adults from countries around the world. It conducted these surveys between the years 2007 and 2010. Based on the results of these surveys, Gallup researchers estimate with 95% confidence that between 22.3% and 25.7% of people worldwide would choose to immigrate to the United States of America. Which of the following is a correct interpretation of the phrase "with 95% confidence"?
a. Adults from 95% of all countries in the world were included in the surveys conducted between 2007 and 2010.
b. Between 22.3% and 25.7% of the people in 95% of the countries that were surveyed would prefer to immigrate to the United States of America.
c. 95% of the time that the same methods are used, the interval estimate will include the true percentage of adults who prefer to immigrate to the United States.
5. In a statistical hypothesis test, we say the data are statistically significant at level α if:
a. α = 0.05
b. α is small.
c. the P-value is less than α.
d. the P-value is larger than α.