a gallup poll in november 2012 found that 54 of the people i

a gallup poll in november 2012 found that 54% of the people in the sample said they wanted to lose weight. The polls margin of error for 95% confidence was 4%. This means that a) the poll used a method that gets an answer within 4% of the truth about the population 95% of the time b) we can be sure that the percent of all adults who want to lose weight is between 50% and 58% c) if Gallup takes another poll using the same method, the results of the second poll will lie between 50% and 58%

Solution

The given problem is a simple case of interpretation of confidence intervals. By the statement \"a 95% CI of mean M of the population is (a,b)\" we mean that if we were to sample 100times from the current population and calculate the values of a and b from each of the samples thenvthe true value of M will be contained in 95 of those calculated intervals from the 100 samples. Nowhere we say that the true value for sure lies within any of those calculated intervals. Nor we can say that when one poll is taken and the interval calculated then the results of the second poll lies in the previously calculated CI. When given that the 95% confident prediction has error margin 4% from the true value then we can only say that about 95% of the number of times the sampling and subsewuent calculation of the interval is done, we get estimated population proportion values within 4% of the true value. i.e part (a) is true.