Is a larger sample size always better? In February 2004, USA Today conducted an online poll. Visitors to their Web site were asked the following question: “Should the U.S. pass a constitutional amendment banning gay marriage?”

Visitors could vote by clicking a button. The results as of 3:30 P.M. on February 25 were that 68.61% voted “No” and 31.39% voted “Yes.” A total of 63,046 votes had been recorded. Using our quick method, we find that the margin of error for 95% confidence for a sample of this size is roughly equal to four-tenths of one percentage point. Is it correct to say that, based on this USA Today online poll, we are 95% confident that 68.61% plus or minus 0.4% of American adults are opposed to having the United States pass a constitutional amendment banning gay marriage? Explain your answer.

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