In 2003, an organization surveyed 1 comma 508 adult Americans and asked about a certain war, "Do you believe the United States made the right or wrong decision to use military force?" Of the 1 comma 508 adult Americans surveyed, 1 comma 085 stated the United States made the right decision. In 2008, the organization asked the same question of 1 comma 508 adult Americans and found that 575 believed the United States made the right decision. Construct and interpret a 90% confidence interval for the difference between the two population proportions, p 2003 minus p 2008.

And the 90% confidence interval would be given (0.310;0.366).  

We are confident at 90% that the difference between the two proportions is between

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

represent the real population proportion for 2003  

represent the estimated proportion for 2003

is the sample size required for 2003

represent the real population proportion for 2008

represent the estimated proportion for 2008

is the sample size required for 2008

represent the critical value for the margin of error  

The population proportion have the following distribution  

The confidence interval for the difference of two proportions would be given by this formula  

For the 90% confidence interval the value of and , with that value we can find the quantile required for the interval in the normal standard distribution.  

And replacing into the confidence interval formula we got:  

And the 90% confidence interval would be given (0.310;0.366).  

We are confident at 90% that the difference between the two proportions is between

boxplot e is the answer