The 2011 Statistical Abstract of the United States includes a table reporting that a national survey in the fall of 2009 found that 11.6% of American adults had played a Sudoku puzzle in the past year. Suppose that these data are based on a sample of 1,000 randomly selected American adults.
a. Use this sample result and a theory-based approach to produce three confidence intervals (90%, 95%, 99%) for the probability that a randomly selected American adult had played a Sudoku puzzle in the past year.
b. How do the midpoints of these three intervals compare?
c. How do the widths of these three intervals compare? Is this what you expected? Explain.
d. Based on the confidence intervals, does the sample result provide strong evidence that more than 10% of all American adults had played a Sudoku puzzle in the past year? Explain.
e. Is it appropriate to use the theory-based approach to find the confidence intervals? Answer this by stating the validity condition, and explain whether or not the condition is satisfied.