The National Sleep Foundation sponsors an annual poll. In a March 2011 press release, they stated "... 63% of Americans say their sleep needs are not being met during the week." The following is an excerpt from the Poll Methodology and Definitions section of the article. "The 2011 Sleep in America® annual poll was conducted for the National Sleep Foundation by WB&A Market Research, using a random sample of 1,508 adults between the ages of 13-64. The margin of error is 2.5 percentage points at the 95% confidence level." Which of the following statements is correct?
a. We are confident that 95% of the 1,508 adults in the sample say their sleep needs are not being met during the week.
b. We are 95% confident that between 60.5% and 655% of Americans say their sleep needs are not being met during the week
c. We are 95% confident that 63% of Americans say their sleep needs are not being met during the week
d. We are 95% confident that between 63% and 655% of Americans say their sleep needs are not being met during the week

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence using data from the sample.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

Sample proportion = 63%

Margin of Error is the width of the confidence interval about the mean.

Margin of error = 2.5%

Confidence level = 95%

Confidence Interval = (Sample proportion) ± (Margin of error)

95% Confidence Interval = (63%) ± (2.5%)

95% Confidence interval = (60.5%, 65.5%)

From the definition of confidence interval given above, we can interpret this confidence interval obtained for the population proportion of Americans that say that their sleep needs are not being met during the week as that;

We are 95% confident that between 60.5% and 65.5% of Americans say their sleep needs are not being met during the week

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